We present cosmological constraints from the sample of Type Ia supernovae SNe Ia discovered and measured during the full 5 yr of the Dark Energy Survey DES SN program. In contrast to most previous cosmological samples in which SNe are classified based on their spectra we classify the DES SNe using a machine learning algorithm applied to their light curves in four photometric bands. Spectroscopic redshifts are acquired from a dedicated followup survey of the host galaxies. After accounting for the likelihood of each SN being an SN Ia we find 1635 DES SNe in the redshift range 0.10 lt z lt 1.13 that pass quality selection criteria sufficient to constrain cosmological parameters. This quintuples the number of highquality z gt 0.5 SNe compared to the previous leading compilation of Pantheon and results in the tightest cosmological constraints achieved by any SN data set to date. To derive cosmological constraints we combine the DES SN data with a highquality external lowredshift sample consisting of 194 SNe Ia spanning 0.025 lt z lt 0.10. Using SN data alone and including systematic uncertainties we find SUBMSUB  0.352  0.017 in flat CDM. SN data alone now require acceleration q SUB0SUB lt 0 in CDM with over 5 confidence. We find inlineformula inlineformula in flat wCDM. For flat w SUB0SUB w SUB a SUBCDM we find inlineformula inlineformula consistent with a constant equation of state to within 2. Including Planck cosmic microwave background Sloan Digital Sky Survey baryon acoustic oscillation and DES 3  2pt data gives SUBMSUB w  0.321  0.007 0.941  0.026. In all cases dark energy is consistent with a cosmological constant to within 2. Systematic errors on cosmological parameters are subdominant compared to statistical errors these results thus pave the way for future photometrically classified SN analyses.
['Cosmology', 'Type Ia supernovae', 'Dark energy', 'Dark matter', '343', '1728', '351', '353', 'Astrophysics - Cosmology and Nongalactic Astrophysics']
The Dark Energy Survey Cosmology Results with 1500 New Highredshift Type Ia Supernovae Using the Full 5 yr Data Set
{'The Dark Energy Survey: Cosmology Results With ∼ 1500 New High-redshift Type Ia Supernovae Using The Full 5-year Dataset': "DES Collaboration: T. M. C. Abbott, 1 M. Acevedo, 2 M. Aguena, 3 A. Alarcon, 4 S. Allam, 5 O. Alves, 6 A. Amon, 7 F. Andrade-Oliveira, 6 J. Annis, 5 P. Armstrong, 8 J. Asorey, 9 S. Avila, 10 D. Bacon, 11 B. A. Bassett, 12, 13 K. Bechtol, 14 P. H. Bernardinelli, 15 G. M. Bernstein, 16 E. Bertin, 17, 18 J. Blazek, 19 S. Bocquet, 20 D. Brooks, 21 D. Brout, 22 E. Buckley-Geer, 23, 5 D. L. Burke, 24, 25 H. Camacho, 26, 3 R. Camilleri, 27 A. Campos, 28 A. Carnero Rosell, 29, 3, 30 D. Carollo, 31 A. Carr, 27 J. Carretero, 10 F. J. Castander, 32, 33 R. Cawthon, 34 C. Chang, 23, 35 R. Chen, 2 A. Choi, 36 C. Conselice, 37, 38 M. Costanzi, 39, 31, 40 L. N. da Costa, 3 M. Crocce, 32, 33 T. M. Davis, 27 D. L. DePoy, 41 S. Desai, 42 H. T. Diehl, 5 M. Dixon, 43 S. Dodelson, 28, 44 P. Doel, 21 C. Doux, 16, 45 A. Drlica-Wagner, 23, 5, 35 J. Elvin-Poole, 46 S. Everett, 47 I. Ferrero, 48 A. Fert'e, 25 B. Flaugher, 5 R. J. Foley, 49 P. Fosalba, 32, 33 D. Friedel, 50 J. Frieman, 5, 35 C. Frohmaier, 51 L. Galbany, 32, 33 J. Garc'ıa-Bellido, 52 M. Gatti, 16 E. Gaztanaga, 11, 32, 33 G. Giannini, 10, 35 K. Glazebrook, 43 O. Graur, 11 D. Gruen, 20 R. A. Gruendl, 50, 53 G. Gutierrez, 5 W. G. Hartley, 54 K. Herner, 5 S. R. Hinton, 27 D. L. Hollowood, 55 K. Honscheid, 56, 57 D. Huterer, 6 B. Jain, 16 D. J. James, 58, 59 N. Jeffrey, 21 E. Kasai, 60, 12 L. Kelsey, 11 S. Kent, 5, 35 R. Kessler, 23, 35 A. G. Kim, 61 R. P. Kirshner, 62, 63 E. Kovacs, 4 K. Kuehn, 64, 65 O. Lahav, 21 J. Lee, 16 S. Lee, 47 G. F. Lewis, 66 T. S. Li, 67 C. Lidman, 68, 8 H. Lin, 5 U. Malik, 8 J. L. Marshall, 41 P. Martini, 56, 69 J. Mena-Fern'andez, 70 F. Menanteau, 50, 53 R. Miquel, 71, 10 J. J. Mohr, 20, 72 J. Mould, 43 J. Muir, 73 A. Moller, 43 E. Neilsen, 5 R. C. Nichol, 74 P. Nugent, 61 R. L. C. Ogando, 75 A. Palmese, 28 Y.-C. Pan, 76 M. Paterno, 5 W. J. Percival, 46, 73 M. E. S. Pereira, 77 A. Pieres, 3, 75 A. A. Plazas Malag'on, 24, 25 B. Popovic, 2 A. Porredon, 78 J. Prat, 35 H. Qu, 16 M. Raveri, 79 M. Rodr'ıguez-Monroy, 80 A. K. Romer, 81 A. Roodman, 24, 25 B. Rose, 2, 82 M. Sako, 16 E. Sanchez, 83 D. Sanchez Cid, 83 M. Schubnell, 6 D. Scolnic, 2 I. Sevilla-Noarbe, 83 P. Shah, 21 J. Allyn. Smith, 84 M. Smith, 85 M. Soares-Santos, 86 E. Suchyta, 87 M. Sullivan, 51 N. Suntzeff, 41 M. E. C. Swanson, 50 B. O. S'anchez, 88 G. Tarle, 6 G. Taylor, 8 D. Thomas, 11 C. To, 56 M. Toy, 51 M. A. Troxel, 2 B. E. Tucker, 8 D. L. Tucker, 5 S. A. Uddin, 89 M. Vincenzi, 2 A. R. Walker, 1 N. Weaverdyck, 6, 61 R. H. Wechsler, 90, 24, 25 J. Weller, 72, 91 W. Wester, 5 P. Wiseman, 51 M. Yamamoto, 2 F. Yuan, 8 B. Zhang, 8 and Y. Zhang 1  \n1 Cerro Tololo Inter-American Observatory, NSF's National Optical-Infrared Astronomy Research Laboratory, Casilla 603, La Serena, Chile  \n2 Department of Physics, Duke University Durham, NC 27708, USA  \n14  \n3 Laborat'orio Interinstitucional de e-Astronomia - LIneA, Rua Gal. Jos'e Cristino 77, Rio de Janeiro, RJ - 20921-400, Brazil 4 Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439, USA 5 Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA 6 Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA 7 Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 8 The Research School of Astronomy and Astrophysics, Australian National University, ACT 2601, Australia 9 Departamento de F'ısica Te'orica and IPARCOS, Universidad Complutense de Madrid, 28040 Madrid, Spain 10 Institut de F'ısica d'Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona) Spain 11 Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK 12 South African Astronomical Observatory, P.O.Box 9, Observatory 7935, South Africa 13 Mathematics Department, University of Cape Town, South Africa Physics Department, 2320 Chamberlin Hall, University of Wisconsin-Madison, 1150 University Avenue Madison, WI 53706-1390 15 Astronomy Department, University of Washington, Box 351580, Seattle, WA 98195, USA 16 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA 17 CNRS, UMR 7095, Institut d'Astrophysique de Paris, F-75014, Paris, France 18 Sorbonne Universit'es, UPMC Univ Paris 06, UMR 7095, Institut d'Astrophysique de Paris, F-75014, Paris, France 19 Department of Physics, Northeastern University, Boston, MA 02115, USA 20 University Observatory, Faculty of Physics, Ludwig-Maximilians-Universitat, Scheinerstr. 1, 81679 Munich, Germany 21 Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK 22 Department of Astronomy and Department of Physics, Boston University Boston, MA 02140, USA 23 Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637, USA Kavli Institute for Particle Astrophysics & Cosmology, P. O. Box 2450, Stanford University, Stanford, CA 94305, USA  \n24 25 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA  \n26 Instituto de F'ısica Te'orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil  \n27 School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia", 'The Dark Energy Survey Collaboration': "28 Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15312, USA  \n29 Instituto de Astrofisica de Canarias, E-38205 La Laguna, Tenerife, Spain 30 Universidad de La Laguna, Dpto. Astrof'ısica, E-38206 La Laguna, Tenerife, Spain 31 INAF-Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, I-34143 Trieste, Italy 32 Institut d'Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain 33 Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain 34 Physics Department, William Jewell College, Liberty, MO, 64068 35 Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA 36 NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA 37 Jodrell Bank Center for Astrophysics, School of Physics & Astronomy, University of Manchester, Oxford Rd, Manchester, M139PL, UK 38 University of Nottingham, School of Physics and Astronomy, Nottingham NG7 2RD, UK 39 Astronomy Unit, Department of Physics, University of Trieste, via Tiepolo 11, I-34131 Trieste, Italy 40 Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy 41 George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, and Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843, USA 42 Department of Physics, IIT Hyderabad, Kandi, Telangana 502285, India 43 Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Victoria 3122, Australia 44 NSF AI Planning Institute for Physics of the Future, Carnegie Mellon University, Pittsburgh, PA 15213, USA 45 Universit'e Grenoble Alpes, CNRS, LPSC-IN2P3, 38000 Grenoble, France 46 Department of Physics and Astronomy, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada 47 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109, USA 48 Institute of Theoretical Astrophysics, University of Oslo. P.O. Box 1029 Blindern, NO-0315 Oslo, Norway 49 Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA 50 Center for Astrophysical Surveys, National Center for Supercomputing Applications, 1205 West Clark St., Urbana, IL 61801, USA 51 School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK 52 Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain 53 Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, IL 61801, USA 54 Department of Astronomy, University of Geneva, ch. d' ' Ecogia 16, CH-1290 Versoix, Switzerland 55 Santa Cruz Institute for Particle Physics, Santa Cruz, CA 95064, USA 56 Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, OH 43210, USA 57 Department of Physics, The Ohio State University, Columbus, OH 43210, USA 58 ASTRAVEO LLC, PO Box 1668, MA 01931, USA 59 Applied Materials Inc., 35 Dory Road, Gloucester, MA 01930, USA 60 Department of Physics, University of Namibia, 340 Mandume Ndemufayo Avenue, Pionierspark, Windhoek, Namibia 61 Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA 62 TMT International Observatory, 100 West Walnut Street, Pasadena CA 91124 63 California Institute of Technology, 1200 East California Boulevard, Pasadena CA 91125 64 Australian Astronomical Optics, Macquarie University, North Ryde, NSW 2113, Australia 65 Lowell Observatory, 1400 Mars Hill Rd, Flagstaff, AZ 86001, USA 66 Sydney Institute for Astronomy, School of Physics, A28, The University of Sydney, NSW 2006, Australia 67 Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto ON, M5S 3H4, Canada 68 Centre for Gravitational Astrophysics, College of Science, The Australian National University, ACT 2601, Australia 69 Department of Astronomy, The Ohio State University, Columbus, OH 43210, USA 70 LPSC Grenoble - 53, Avenue des Martyrs 38026 Grenoble, France 71 Instituci'o Catalana de Recerca i Estudis Avan¸cats, E-08010 Barcelona, Spain 72 Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse, 85748 Garching, Germany 73 Perimeter Institute for Theoretical Physics, 31 Caroline St. North, Waterloo, ON N2L 2Y5, Canada 74 School of Mathematics and Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK 75 Observat'orio Nacional, Rua Gal. Jos'e Cristino 77, Rio de Janeiro, RJ - 20921-400, Brazil 76 Graduate Institute of Astronomy, National Central University, 300 Jhongda Road, 32001 Jhongli, Taiwan 77 Hamburger Sternwarte, Universitat Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany 78 Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute, 44780 Bochum, Germany 79 Department of Physics, University of Genova and INFN, Via Dodecaneso 33, 16146, Genova, Italy 80 Laboratoire de physique des 2 infinis Ir'ene Joliot-Curie, CNRS Universit'e Paris-Saclay, Bˆat. 100, F-91405 Orsay Cedex, France 81 Department of Physics and Astronomy, Pevensey Building, University of Sussex, Brighton, BN1 9QH, UK 82 Department of Physics, Baylor University, One Bear Place #97316, Waco, TX 76798-7316, USA 83 Centro de Investigaciones Energ'eticas, Medioambientales y Tecnol'ogicas (CIEMAT), Madrid, Spain  \n84 Austin Peay State University, Dept. Physics, Engineering and Astronomy, P.O. Box 4608 Clarksville, TN 37044, USA 85 Physics Department, Lancaster University, Lancaster, LA1 4YB, UK  \n86 University of Zurich, Physics Institute, Winterthurerstrasse 190/Building 36, 8057 Zurich, Switzerland  \n87 Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831  \n88 Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France  \n89 Centre for Space Studies, American Public University System, 111 W. Congress Street, Charles Town, WV 25414, USA 90 Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA", 'ABSTRACT': 'We present cosmological constraints from the sample of Type Ia supernovae (SN Ia) discovered and measured during the full five years of the Dark Energy Survey (DES) Supernova Program. In contrast to most previous cosmological samples, in which supernovae are classified based on their spectra, we classify the DES supernovae using a machine learning algorithm applied to their light curves in four photometric bands. Spectroscopic redshifts are acquired from a dedicated follow-up survey of the host galaxies. After accounting for the likelihood of each supernova being a SN Ia, we find 1635 DES SNe in the redshift-range 0 . 10 < z < 1 . 13 that pass quality selection criteria sufficient to constrain cosmological parameters. This quintuples the number of high-quality z > 0 . 5 SNe compared to the previous leading compilation of Pantheon+, and results in the tightest cosmological constraints achieved by any supernova data set to date. To derive cosmological constraints we combine the DES supernova data with a high-quality external low-redshift sample consisting of 194 SNe Ia spanning 0 . 025 < z < 0 . 10. Using supernova data alone and including systematic uncertainties we find Ω M = 0 . 352 ± 0 . 017 in flat-ΛCDM. Supernova data alone now require acceleration ( q 0 < 0 in ΛCDM) with over 5 σ confidence. We find (Ω M , w ) = (0 . 264 +0 . 074 -0 . 096 , -0 . 80 +0 . 14 -0 . 16 ) in flatw CDM. For flatw 0 w a CDM, we find (Ω M , w 0 , w a ) = (0 . 495 +0 . 033 -0 . 043 , -0 . 36 +0 . 36 -0 . 30 , -8 . 8 +3 . 7 -4 . 5 ), consistent with a constant equation of state to within ∼ 2 σ . Including Planck CMB, SDSS BAO, and DES 3 × 2-point data gives (Ω M , w ) = (0 . 321 ± 0 . 007 , -0 . 941 ± 0 . 026). In all cases dark energy is consistent with a cosmological constant to within ∼ 2 σ . Systematic errors on cosmological parameters are subdominant compared to statistical errors; these results thus pave the way for future photometrically classified supernova analyses.  \nKeywords: supernovae, cosmology, dark energy', '1. INTRODUCTION': "The standard cosmological model posits that the energy density of the Universe is dominated by dark components that have not been detected in terrestrial experiments and thus do not appear in the standard model of particle physics. Known as cold dark matter and dark energy, their study represents an opportunity to deepen our understanding of fundamental physics.  \nThe Dark Energy Survey (DES) was conceived to characterize the properties of dark matter and dark energy with unprecedented precision and accuracy through four primary observational probes (The Dark Energy Survey Collaboration 2005; Bernstein et al. 2012; Dark Energy Survey Collaboration 2016; Lahav et al. 2020). One of these four probes is the Hubble diagram (redshift-distance relation) for Type Ia supernovae (SNe Ia), which act as standardizable candles (Rust 1974; Pskovskii 1977; Phillips et al. 1999) to constrain the history of the cosmic expansion rate. To imple-  \nment this probe, the DES SN survey was designed to provide the largest, most homogeneous sample of highredshift supernovae ever discovered. The two papers that first presented evidence for the accelerated expansion of the universe (Riess et al. 1998; Perlmutter et al. 1999) used a total of 52 high-redshift supernovae with sparsely sampled light-curve measurements in one or two optical passbands. Building on two decades of subsequent improvements in SN surveys and analysis, we present here the cosmological constraints using the full 5-year DES SN dataset, consisting of well-sampled, precisely calibrated light curves for 1635 new high-redshift supernovae observed in four bands g, r, i, z .  \nFor the last decade, SN Ia cosmology constraints have largely come from combining data from many surveys. The recent Pantheon+ analysis (Scolnic et al. 2022; Brout et al. 2022a) combined three separate midz samples (0 . 1 < z < 1 . 0), 11 different lowz samples ( z < 0 . 1), and four separate highz samples ( z > 1 . 0),  \neach with different photometric systems and selection functions (Gilliland et al. 1999; Hicken et al. 2009; Riess et al. 2001, 2004, 2007; Sullivan et al. 2011; Hicken et al. 2012; Suzuki et al. 2012; Ganeshalingam et al. 2013; Betoule et al. 2014; Krisciunas et al. 2017; Foley et al. 2017; Riess et al. 2018; Sako et al. 2018; Brout et al. 2019b; Smith et al. 2020a). The DES sample, which rivals in number the entirety of Pantheon+, does not have the low-redshift ( z < 0 . 1) coverage to completely remove the need for external lowz samples, but at higher redshift enables us to replace a heterogeneous mix of samples with a homogeneous sample of high quality, wellcalibrated light curves.  \nA key aim of the DES analysis was to minimize systematic (relative to statistical) errors to enable a robust analysis. Vincenzi et al. (2024) shows that our error budget is dominated by statistical uncertainty, in contrast to most SN cosmology analyses of the last decade, for which the systematic uncertainties equalled or exceeded the statistical uncertainties (Betoule et al. 2014; Scolnic et al. 2018; Dark Energy Survey Collaboration 2019). We also highlight that the most critical sources of systematics are those related to the lack of a homogeneous and well calibrated lowz sample.  \nAs the DES sample enables a SN Ia measurement of cosmological parameters that is largely independent of previous SN cosmology analyses, we have been careful to 'blind' our analysis (see Sec. 2.3). The analysis work described in Vincenzi et al. (2024), which stops just short of constraining cosmological parameters, was shared widely with the DES collaboration, evaluated, and approved before unblinding. Unblinding standards included multiple validation checks with simulations and full accounting and explanation of the error budget. No elements of the analysis were changed after unblinding.  \nIn this paper we review the analysis of the complete DES SN dataset (as detailed in many supporting papers; see Fig. 1) and present the cosmological results. An important advance on most previous analyses is that we use a photometrically classified rather than spectroscopically classified sample (Moller & de Boissi'ere 2020; Qu et al. 2021), and implement advanced techniques to classify SN Ia and incorporate classification probabilities in the cosmological parameter estimation (Kunz et al. 2007, 2012; Hlozek et al. 2012). While this advance increases the complexity of the analysis, in this work and previous papers (Vincenzi et al. 2023; Moller et al. 2022) we show that the impact of non-SN Ia contamination due to photometric misclassification is well below the statistical uncertainty on cosmological parameters, and this constitutes one of the key results of our analysis.", 'Data:': '- -Calibration (Burke et al. 2018, Brout et al. 2022, Rykoff et al. 2023)\n- -SN photometry (Brout et al. 2019, Sanchez et al. 2024)\n- -SN spectroscopy (Smith et al. 2020a)\n- -DCR and chrom (Lasker et al. 2018, Lee&Acevedo et al. 2023)\n- -Host galaxy redshifts and properties (Lidman et al. 2020, Carr et\n- al. 2021, Wiseman et al.  2020/2021, Kelsey et al. 2023)', 'Simulations:': '-Survey selection effects (Kessler et al. 2019a, Vincenzi et al. 2020) -SN Ia intrinsic and dust properties (Brout&Scolnic 2021, Popovic et al. 2021a/b, Wiseman et al. 2022) and rates (Wiseman et al. 2021) -Contamination (Vincenzi et al. 2019/2020, Kessler et al. 2019b)', 'Analysis:': "Pipeline and Overview  \n( Hinton et al. 2020, Vincenzi et al. 2024)  \n- - Light-curve fitting (Taylor et al. 2023)\n- - SN classification  (Möller & de Boissière 2020,  Qu et al. 2021,\n- Vincenzi et al. 2021, Moller et al. 2022)\n- - 'BEAMS' and bias corrections (Kessler & Scolnic 2017), unbinning\n- the SN Hubble diagram (Brout et al. 2020, Kessler et al. 2023)\n- - Effects of host galaxy mismatch (Qu et al. 2023)\n- - Cosmological contour validation (Armstrong et al. 2023)", 'Cosmological results: DES Collaboration 2024': "Testing non-standard cosmological models (Camilleri et al. 2024)  \nFigure 1. Overview of supporting papers for DES-SN5YR cosmological results.  \nCombining our DES data with a low-redshift sample (see Sec. 2), we fit the Hubble diagram to test the standard cosmological model as well as multiple common extensions including spatial curvature, non-vacuum dark energy, and dark energy with an evolving equation of state parameter. In Camilleri et al. (in prep. 2024) we present fits to more exotic models.  \nThe structure of the paper is as follows. We begin in Sec. 2 by describing the dataset, its acquisition, reduction, calibration, and light-curve fitting. We summarize the models we test in Sec. 3 before presenting the results in Sec. 4; our discussion and conclusions follow in Sec. 5 and Sec. 6. The details of our data release, which includes the code needed to reproduce our results, appear in S'anchez (in prep. 2024).", '2.1. DES and Low-redshift SNe': "Our primary dataset is the full five years of DES SNe, which we combine with a historical set of nearby supernovae from CfA3 (Hicken et al. 2009), CfA4 (Hicken et al. 2012), CSP (Krisciunas et al. 2017, DR3) and the  \nFigure 2. All DES light curves, showing observed magnitudes in g , r , i , and z bands (left to right respectively) normalized by the maximum brightness of each light curve, and with the time-axis de-redshifted to the rest-frame. Each light curve has been arbitrarily offset by their redshift, with higher-redshift objects higher on the plot (as labeled on vertical axis). Lines show best-fit SALT3 light-curve fits. The g -band and r -band light curves are not used above z ∼ 0 . 4 and z ∼ 0 . 85 respectively because that corresponds to the redshifts at which the lower-wavelength limit of the SALT3 model (3500 ˚ A in the rest frame) passes out of their observed wavelength ranges.  \n<!-- image -->  \nFoundation SN sample (Foley et al. 2017). We refer to the combined DES plus historical dataset as DESSN5YR .  \nThe DES supernova program was carried out over five seasons, August to February from 2013-2018, during which we observed ten ∼ 3 deg 2 fields with approximately weekly cadence in four bands ( g, r, i, z ). Eight of the fields were observed to 5 σ depth of ∼ 23 . 5 mag in all four bands (shallow fields) and two to a deeper limit of ∼ 24 . 5 mag (deep fields). See Flaugher et al. (2015) for a summary of the Dark Energy Camera, Smith et al. (2020a) for a summary of the supernova program, and Diehl et al. (2016, 2018) for observational details.  \nThe DES SNe were discovered via difference imaging (Kessler et al. 2015) based on the method of Alard & Lupton (1998). DES images are calibrated following the Forward Global Calibration Method (FGCM; Burke et al. 2018; Sevilla-Noarbe et al. 2021; Rykoff 2023), and both DES and lowz samples are recalibrated as part of the SuperCal-Fragilistic cross calibration effort described in Brout et al. (2022b). SN fluxes are determined using scene modeling photometry (Brout et al. 2019b); we include corrections from spectral energy distribution variations (Burke et al. 2018; Lasker et al. 2019) and from differential chromatic refraction and wavelengthdependent seeing (Lee & Acevedo et al. 2023). We esti-  \nFigure 3. Histogram showing the redshift distribution of the DES-SN5YR sample, with new DES SNe in blue and our lowz sample in red. For comparison the distribution of redshifts in the existing Pantheon+ sample is shown in grey (Brout et al. 2022a), which also includes the DES SNe from the DES-SN3YR analysis (blue dashed line). The five-year DES sample contains ∼ 4 × more supernovae above z ∼ 0 . 4 than the Pantheon+ compilation.  \n<!-- image -->  \nmate the overall accuracy of our calibrated photometry to be ≲ 5 mmag. Host galaxies are assigned following the directional light radius (DLR) method (Sullivan et al. 2006; Gupta et al. 2016; Qu et al. 2023), and host galaxy properties are determined as described by Kelsey et al. (2023) based on Fioc & Rocca-Volmerange (1999) using deep coadded images by Wiseman et al. (2020). Host galaxy spectroscopic redshifts are obtained primarily within the OzDES programme (Yuan et al. 2015; Childress et al. 2017; Lidman et al. 2020). The final data release of photometry of ∼ 20 , 000 candidates, redshifts of hosts, and host galaxy properties is presented in S'anchez (in prep. 2024).  \nWe apply strict quality cuts to this sample of candidates to select our final high-quality sample for the Hubble diagram. The same quality cuts were applied to both the lowz sample and the DES supernovae. First, we require a spectroscopic redshift of the host galaxy, good light-curve coverage (at least two detections with SNR > 5 in two different bands), and a well converged light-curve fit using the SALT3 model 1 (Kenworthy et al. 2021; Taylor et al. 2023); this reduces the DES sample size to 3621. Additional requirements include light-curve parameters (stretch and colour) within normal range for SNe Ia, a well-constrained time of peak brightness (uncertainty less than 2 days), good SALT3 fit-probability, and valid distance-bias correction from our simulation (see Table 4 of Vincenzi et al. 2024, for  \nmore detail). Our final Hubble-diagram sample includes 1635 supernovae, of which 1499 have a machine-learning probability of being a Type Ia greater than 50% (see Sec. 2.2). Note that we do not perform a cut on this machine-learning probability, rather we use it in the BEAMS formalism that produces our Hubble diagram and to weight the SN distance uncertainties in the fits to the final Hubble diagram (Kessler et al. 2023). The set of all DES light curves is visualised in Fig. 2.  \nSince we focus on minimizing potential systematic errors, we only use the best-calibrated, most homogeneous sample of lowz SNe Ia. To reduce the impact of peculiar velocity uncertainties we remove SNe with z < 0 . 025. We furthermore combine only a subset of the available low-redshift samples: CfA3&4, CSP, and Foundation SNe, which are the four largest lowz samples with the most well-understood photometric calibration. Our lowz sample thus totals 194 SNe with z < 0 . 1; this can be compared to Pantheon+, for which the lowz sample was almost four times larger (741 SNe at z < 0 . 1). We have thus exchanged the statistical constraining power of more lowz SNe for better control of systematics. The redshift distribution of our sample compared to the compilation of historical samples in Pantheon+ is shown in Fig. 3. To conclude, the final DES-SN5YR sample includes 1635 DES SNe and 194 lowz external SNe, for a total of 1829 SNe.", '2.2. From light curves to Hubble diagram': "A critical step in the cosmology analysis is to convert each supernova's light curve (magnitude vs time in multiple bands; see examples in Fig. 2) to a single calibrated number representing its standardized magnitude and estimated distance modulus.  \nTo achieve this, we use the SALT3 light-curve fitting model as presented in Kenworthy et al. (2021); Taylor et al. (2023) and retrained in Vincenzi et al. (2024) to determine the light-curve fit parameters, amplitude of the SN flux ( x 0 ), stretch ( x 1 ), and color ( c ). These fitted parameters are used to estimate the distance modulus, µ ≡ m -M , using an adaptation of the Tripp equation (Tripp 1998) that includes a correction for observed correlations between SN Ia luminosity and host properties, γG host = ± γ/ 2. Here γ is the size of the step and G host is the property of the host galaxy that is used to determine the step (i.e. mass or color); the sign is + if G host is above the step or -if below. This correction has historically been described as a 'mass step' but we also consider the possibility that it is a 'color step' (see Sec. 2.2 of Vincenzi et al. 2024),  \nµ obs ,i = m x,i + αx 1 ,i -βc i + γG host ,i -M -∆ µ bias ,i , (1)  \nFigure 4. Hubble diagram of DES-SN5YR. We show both the single SN events and the redshift-binned SN distance moduli. Redshift bins are adjusted so that each bin has the same number of SNe ( ∼ 50). The 1635 new DES supernovae are in blue, and in the upper panel they are shaded by their probability of being a Type Ia; most outliers are likely contaminants (pale blue). The inset shows the number of SNe as a function of redshift (same z -range as the main plot). The lower panel shows the difference between the data and the best fit Flatw CDM model from DES-SN5YR alone (third result in Table 2), and overplots three other best fit cosmological models - Flat-ΛCDM model from DES-SN5YR alone (magenta line, first result in Table 2), Flatw 0 w a CDM model from DES-SN5YR alone (green line, fourth result in Table 2), and Planck 2020 Flat-ΛCDM model without SN data (dashed line, Ω Planck M =0 . 317 ± 0 . 008).  \n<!-- image -->  \nwhere m x = -2 . 5 log 10 ( x 0 ). 2 The constants α , β , and γ are global parameters determined from the likelihood analysis of all the SNe on the Hubble diagram, while the terms subscripted by i refer to parameters of individual SNe. We find α = 0 . 161 ± 0 . 001, β = 3 . 12 ± 0 . 03, and γ = 0 . 038 ± 0 . 007. We marginalize over the absolute magnitude M (see Sec. 3). The final term in Eq. 1 accounts for selection effects, Malmquist bias, and light curve fitting bias.  \nThe nuisance parameters and ∆ µ bias ,i term in Eq. 1 are determined using the 'BEAMS with Bias Corrections' (BBC) framework (Kessler & Scolnic 2017). In particular, bias corrections ∆ µ bias ,i are estimated from a large simulation of our sample. The simulation models the rest-frame SN Ia spectral energy distribution (SED) at all phases, SN correlations with host-galaxy  \nproperties, SED reddening through an expanding universe, broadband griz fluxes, and instrumental noise (see Fig. 1 in Kessler et al. 2019a). Using Eq. 1 there remains intrinsic scatter of ∼ 0 . 1 mag in Hubble residuals. Following the numerous recent studies on understanding and modelling SN Ia dust extinction and progenitors (Wiseman et al. 2021, 2022; Duarte et al. 2022; Dixon et al. 2022; Chen et al. 2022; Meldorf et al. 2023), we model this residual scatter using the dust-based model from Brout & Scolnic (2021) [BS21]; Popovic et al. (2023a). In contrast to previously used models in K13, the BS21 model accurately models the Hubble residual bias and scatter as a function of the fitted SALT2 color (see Fig. 5 in Vincenzi et al. (2024), and Fig. 6 in Brout & Scolnic (2021)). Due to uncertainties in the fitted dust parameters (Popovic et al. 2023a), this intrinsic scatter model remains the largest source of systematic uncertainty from the simulation.  \nAs we do not spectroscopically classify the SNe and thus expect contamination from core-collapse (CC) supernovae, we perform machine learning light-curve clas-  \nsification on the sample following Vincenzi et al. (2023); Moller et al. (2022). We implement two advanced machine learning classifiers, SuperNNova (Moller & de Boissi'ere 2020) and SCONE (Qu et al. 2021) and use state-of-the-art simulations to model contamination (estimated to be ∼ 6 . 5%, see Table 10 and Sec. 7.1.5 of Vincenzi et al. 2024). Classifiers are trained using corecollapse and peculiar SN Ia simulations based on Vincenzi et al. (2021) and using state-of-the-art SED templates by Vincenzi et al. (2019); Kessler et al. (2019b). These DES simulations are the first to robustly reproduce the contamination observed in the Hubble residuals (Vincenzi et al. 2021; Vincenzi et al. 2024, Table 10).  \nFor each SN, the trained classifiers assign a probability of being a Type Ia, and these probabilities are included within the BEAMS framework to marginalize over corecollapse contamination and produce the final Hubble Diagram (Kunz et al. 2012; Hlozek et al. 2012). The final DES-SN5YR Hubble diagram is shown in Fig. 4 and includes 1829 SNe.  \nAs discussed in Kessler et al. (2023); Vincenzi et al. (2024), the probability that each supernova is a Type Ia ( P Ia ) is incorporated in the BBC fit and used to calculate a BEAMS probability, P B(Ia) (see Eq. 9 in Kessler et al. 2023). BEAMS probabilities are used to inflate distance uncertainties of likely contaminants by a factor ∝ 1 / √ P B(Ia) (see Eq. 10 in Vincenzi et al. 2024). Therefore, the released Hubble diagram data includes distance bias corrections and inflated distance uncertainties (see App. A), enabling users to fit the Hubble diagram without applying additional corrections. With this BEAMS uncertainty weight, we find 75 SNe with distance modulus uncertainties σ µ,i, final > 1 mag and 1331 SNe with σ µ,i, final < 0 . 2 mag. 3  \nVincenzi et al. (2024) stops short of performing cosmological constraints but provides the corrected distance moduli µ along with their uncertainties σ µ , redshifts for each SN, and a statistical+systematic covariance matrix C , which we describe further in Sec. 3.  \nArmstrong et al. (2023) presents validation of the cosmological contours produced by our pipeline. Validation that our analysis pipeline is insensitive to the cosmological model assumed in our bias correction simulation appears in Camilleri et al. (in prep. 2024).", '2.3. Unblinding criteria': "Throughout our analysis, cosmological parameters estimated from real data were blinded. We validate our entire pipeline on detailed catalogue-level simulations and examine the cosmological parameters estimated from simulations to test that the input cosmology is recovered. In addition to the many tests described in Vincenzi et al. (2024), the final unblinding criteria that our data passed were:  \n- · Accuracy of simulations: Reduced χ 2 between the distribution of data and simulations across a variety of observables (redshift, SALT3 parameters and goodness of the fit, maximum signal-tonoise ratio at peak, host stellar mass) is required to be between 0.7 and 3.0 (see Vincenzi et al. 2024, Fig. 3-4).\n- · Pipeline validation using DES simulations: Demonstrate that our pipeline recovers the input cosmology. We produce 25 data-size simulated samples (statistically independent) assuming a Flat-ΛCDM universe with best-fit Planck value of Ω M and analyze them the same way as real data. We fit each Hubble diagram assuming a Flatw CDM model with a Planck prior and find a mean bias of w -w true ≃ 0 . 001 ± 0 . 020, where w is the mean value of the marginalized posterior of the dark energy equation of state parameter over the 25 samples, and w true = -1 is the model value of that parameter input to the simulation.\n- · Validation of contours: ensuring that our uncertainty limits accurately represent the likelihood of the models (Armstrong et al. 2023).\n- · Independence of reference cosmology: ensuring that our results are sufficiently independent of cosmological assumptions that enter our bias correction simulations (Camilleri et al. in prep. 2024).\n- 2.4. Combining SN with other cosmological probes  \nWecombine the DES-SN5YR cosmological constraints with measurements from other complementary cosmological probes. In particular, we use:  \n- · Cosmic Microwave Background (CMB) measurements of the temperature and polarisation power spectra (TTTEEE) presented by the Planck Collaboration (2020). We use the Python implementation of Planck's 2015 Plik lite (Prince & Dunkley 2019).\n- · Weak lensing and galaxy clustering measurements from the DES3 × 2pt year-3 magnitude-limited  \nTable 1. Variations on the standard cosmological model that are tested in this paper, their Friedmann Equations, and the free parameters in the fit.  \n(MagLim) lens sample; 3 × 2-point refers to the simultaneous fit of three 2-point correlation functions, namely galaxy-galaxy, galaxy-lensing, and lensing-lensing correlations (Dark Energy Survey Collaboration 2022, 2023).  \n- · Baryon acoustic oscillation (BAO) measurements as presented in the extended Baryon Oscillation Spectroscopic Survey paper (eBOSS; Dawson et al. 2016; Alam et al. 2021), which adds the BAO results from SDSS-IV (Blanton et al. 2017) to earlier SDSS BAO data. Specifically, we use 'BAO' to refer to the BAO-only measurements from the Main Galaxy Sample (Ross et al. 2015), BOSS (SDSS-III Alam et al. 2017), eBOSS LRG (Bautista et al. 2021), eBOSS ELG (de Mattia et al. 2021), eBOSS QSO (Hou et al. 2021), and eBOSS Lya (du Mas des Bourboux et al. 2020).  \nWhen combining these data we run simultaneous MCMC fits of the relevant data vectors. We present three combinations: the simplest CMB-dependent combination CMB+SN, a CMB-independent combination BAO+3 × 2pt+SN, and a combination of them all.", '3. MODELS AND THEORY': 'We present cosmological results for the standard cosmological model - flat space with cold dark matter and a cosmological constant (Flat-ΛCDM) - and some basic extensions, such as relaxing the assumption of spatial flatness (ΛCDM), allowing for constant equation of state parameter ( w ) of dark energy (Flatw CDM), and including a linear parameterisation for time-varying dark energy (Flatw 0 w a CDM) in which the equation of state parameter is given by w = w 0 + w a (1 -a ) (Chevallier & Polarski 2001; Linder 2003).  \nTo calculate the theoretical distance as a function of redshift we begin with the comoving distance,  \nR 0 χ (¯ z ) = c H 0 ∫ ¯ z 0 dz E ( z ) , (2)  \nwhere ¯ z is the redshift due to the expansion of the Universe, E ( z ) ≡ H ( z ) /H 0 is the normalized redshift-  \nendent expansion rate and is given for each cosmological model by the expression in Table 1, R 0 = c/ ( H 0 √ | Ω K | ) is the scale factor with dimensions of distance (where subscript 0 indicates its value at the present day), and Ω K ≡ 1 -Ω M -Ω Λ is the curvature term. The dimensionless scale factor ( a ≡ R/R 0 ) at the time of emission for an object with cosmological redshift ¯ z is a = 1 / (1 + ¯ z ). The luminosity distance is given by,  \nD L ( z obs , ¯ z ) = (1 + z obs ) R 0 S k ( χ (¯ z )) , (3)  \nwhere z obs is the observed redshift, and the curvature is captured by S k ( χ ) = sin χ , χ , and sinh χ for closed (Ω K < 0), flat (Ω K = 0), and open (Ω K > 0) universes respectively. 4  \nTo compare data (Eq. 1) to theory we calculate the theoretical distance modulus, which is dependent on the set of cosmological parameters we are interested in (Θ, given in the right column of Table 1),  \nµ ( z, Θ) = 5 log 10 ( D L ( z, Θ) / 1 Mpc) + 25 . (4)  \nWe compute the difference between data and theory for every i th supernova, ∆ µ i = µ obs ,i -µ ( z i , Θ), and find the minimum of  \nχ 2 = ∆ µ i C -1 ij ∆ µ T j , (5)  \nwhere C -1 is the inverse covariance matrix (including both statistical and systematic errors) of the ∆ µ vector (see Sec. 3.6 of Vincenzi et al. 2024).  \nThe uncertainty covariance matrix includes a diagonal statistical term (discussed Sec. 2.2) and a systematic term. The systematic covariance matrix is built following the approach in Conley et al. (2011) and accounts for systematics such as calibration, intrinsic scatter, and redshift corrections (see Table 6 of Vincenzi et al. 2024). Each element of the covariance matrix expresses the covariance between two of the SNe in the sample. The covariance matrix has dimensions of the number of supernovae N SNe × N SNe and we follow the formalism introduced by Brout et al. (2021) and Kessler et al. (2023).  \nFinally, the absolute magnitude of SNe Ia ( M ) and the H 0 parameter (which appears in the luminosity distance) are completely degenerate and therefore they are combined in the single parameter M = M + 5 log 10 ( c/H 0 ). All of our cosmology results are marginalized over this term. Therefore, the value of H 0 has no impact on the fitting of our cosmological results, and we do not constrain H 0 . While M has no impact on cosmology fitting, a precise value is needed to simulate bias corrections. The M uncertainty is below 0.01, resulting in a negligible impact on bias corrections (Brout et al. 2022a; Camilleri et al. in prep. 2024).', '4. RESULTS': 'With the new DES high-redshift supernova sample we can put strong constraints on cosmological models. Of particular interest is whether dark energy is consistent with a cosmological constant or whether its density and/or equation of state parameter varies over the wide redshift range of our sample. The results of our cosmological fits are outlined in this section and summarized in Table 2, and their implications are explored in Sec. 5.  \nWe estimate cosmological constraints using Markov Chain Monte Carlo (MCMC) methods as implemented in the CosmoSIS framework (Zuntz et al. 2015), the samplers emcee for best fits (Foreman-Mackey et al. 2013), and PolyChord for tension metrics (Handley et al. 2015), 5 except for fits that include BAO+3 × 2pt, which are calculated using PolyChord for both best fit and tensions. 6 For all fits we present the median of the marginalized posterior and cumulative 68.27% confidence intervals. The chains and code (with the flexibility to test other statistical choices) are publicly available (see Appendix A). Figs. 5, 6, 7 and 8 all present the joint probability contours for 68.3% and 95.5%.', '4.1. Constraints on Cosmological Parameters': 'Figure 5. Constraints on matter density in the FlatΛCDM model from DES-SN5YR only (cyan), DES-SN5YR combined with CMB constraints from Planck Collaboration (2020) (blue), and DES-SN5YR combined with BAO+3 × 2pt (orange), and all probes combined (DESSN5YR+BAO+3 × 2pt and CMB constraints, red). CMB constraints only and BAO+3 × 2pt constraints alone are also shown for comparison (dashed and dotted-dashed respectively).  \n<!-- image -->', '4.1.1. FlatΛ CDM': 'For the simplest parameterization, Flat-ΛCDM, Ω M is the only free parameter. We show the probability density function (PDF) of this constraint for DES-SN5YR in Fig. 5; we measure a value of Ω M =0 . 352 ± 0 . 017. We also show the probability distribution of the Planck Collaboration (2020) measurement of Ω Planck M =0 . 317 ± 0 . 008. These are approximately 7 2 σ apart, but not in significant tension as discussed in Sec 4.2.  \nCombining DES-SN5YR with Planck CMB gives Ω M =0 . 338 +0 . 016 -0 . 014 , while combining with BAO+3 × 2pt gives Ω M =0 . 330 +0 . 011 -0 . 010 . Combining all three gives Ω M =0 . 315 ± 0 . 007. Interestingly, the combination of all data sets (red in Fig. 5) gives a lower Ω M than any of the other combinations. The reason can be seen in Fig. 6, where all constraints cross the Flat Universe line to the upper left of any individual best fit.  \n<!-- image -->  \nM  \nFigure 6. Constraints for ΛCDM model (non-zero curvature allowed) from the DES-SN5YR dataset only (cyan), from DES-SN5YR combined with BAO+3 × 2pt (orange), from DES-SN5YR combined with CMB measurements (blue), and from all these combined (red). For comparison, we also present cosmological constraints from Planck Collaboration (2020) only (black dashed).Figure 7. Same as Fig. 6 but for the Flat w CDM model. The horizontal dotted line marks the equation of state values for a cosmological constant, i.e. w = -1.  \n<!-- image -->', '4.1.2. Λ CDM': 'Fitting DES-SN5YR to the ΛCDM model, we find (Ω M , Ω Λ )=(0 . 291 +0 . 063 -0 . 065 , 0 . 55 ± 0 . 17), consistent with a flat universe (Ω K =0 . 16 ± 0 . 16); see Fig. 6. Combining DES-SN5YR with BAO+3 × 2pt is also consistent with a flat Universe, with uncertainties on Ω K reduced to ∼ ± 0 . 034, while the combination with Planck gives Ω K =0 . 010 ± 0 . 005. The combination of all three gives Ω K =0 . 002 +0 . 004 -0 . 003 .', '4.1.3. Flatw CDM': "Fitting DES-SN5YR to the Flatw CDM model, we measure (Ω M , w ) = (0 . 264 +0 . 074 -0 . 096 , -0 . 80 +0 . 14 -0 . 16 ); see Fig. 7. This is consistent with a cosmological constant (within 2 σ ), although our data favors a w -value that is slightly larger than -1.  \nThe w -Ω M contours from SN alone are highly nonGaussian with a curved 'banana'-shaped degeneracy. The best fit value for w or Ω M is thus an insufficient summary of the SN information, as a small shift along the degeneracy direction can result in large shifts in the best-fit values. To address this issue, in Camilleri et al. (in prep. 2024) we introduce a new parameter, Q H ( z ) ≡ -a/ ( aH 2 0 ) ≡ q ( H/H 0 ) 2 . This combination of the deceleration parameter q and the Friedmann equation H/H 0 follows the curve of the degeneracy in the w -Ω M plane. Therefore, measuring Q H ( z ) summarizes the supernova information in a single, almost degeneracy-free value. 8 One has to choose the redshift at which one quotes Q H ( z ), to best match the angle of the degeneracy for the redshift range of the sample. We find Q H ( z = 0 . 2) = -0 . 340 ± 0 . 032 using DES-SN5YR only (see Camilleri et al. in prep. 2024). This Q H value can be used to roughly approximate the DES-SN5YR results and characterize the constraining power without the need for a full fit to the Hubble diagram.  \nThe degeneracy in the w -Ω M plane is broken by combining SNe with external probes. Combining with Planck, we measure (Ω M , w ) = (0 . 337 +0 . 013 -0 . 011 , -0 . 955 +0 . 032 -0 . 037 ), again within 2 σ of a cosmological constant. Planck alone provides only a loose constraint on the equation of state parameter of dark energy, w Planck = -1 . 51 +0 . 27 -0 . 18 ; combining with DESSN5YR reduces the uncertainty significantly due to the different degeneracy direction, demonstrating the combined constraining power of these two complementary probes.  \nCombining DES-SN5YR with BAO+3 × 2pt we find w = -0 . 922 +0 . 035 -0 . 037 , slightly over 2 σ from the cosmologi-  \nFigure 8. Same as Fig. 6 but for the Flatw 0 w a CDM model. The dashed crosshairs mark the equation of state values for a cosmological constant, i.e. ( w 0 , w a ) = ( -1 , 0). The residuals between the DES-SN5YR best fit Flatw 0 w a CDM w.r.t. the Flatw CDM model are presented in Fig. 4.  \n<!-- image -->  \nl constant. This data combination demonstrates that these late-universe probes alone provide constraints that are consistent with - and of comparable constraining power to - the combination of SN and CMB data. The full combination of all data sets gives w = -0 . 941 ± 0 . 026.", '4.1.4. Flatw 0 w a CDM': "Fitting DES-SN5YR alone to the Flatw 0 w a CDM model gives an equation of state that is slightly over 2 σ from a cosmological constant, marginally preferring a time-varying dark energy (Ω M , w 0 , w a ) =(0 . 495 +0 . 033 -0 . 043 , -0 . 36 +0 . 36 -0 . 30 , -8 . 8 +3 . 7 -4 . 5 ); see Fig. 8.  \nCombining DES-SN5YR and the CMB, we find (Ω M , w 0 , w a ) =(0 . 325 +0 . 016 -0 . 012 , -0 . 73 ± 0 . 11, -1 . 17 +0 . 55 -0 . 62 ), which again deviates slightly from the cosmological constant. The same trend is seen when combining with BAO+3 × 2pt and with all data combined. The negative w a means that the dark energy equation of state parameter is increasing with time (sometimes referred to as a 'thawing' model).  \nGoodness of fit and tension  \n4.2.1. χ per degree of freedom  \n4.2. 2  \nTo assess whether our best fits are good fits we calculate the χ 2 per degree of freedom for all our dataset and model combinations; see the last column of Table 2. The χ 2 we use for this test is the maximum likelihood of the entire parameter space, not the marginalized best fit for each parameter.  \nThe number of degrees of freedom is the number of data points minus the number of parameters that are common to all datasets (i.e., the cosmological parameters of interest). The number of data points added by the CMB, BAO, and 3 × 2pt is respectively 615, 8, and 471. Due to our treatment of contamination (by inflating the uncertainties of SNe with a low P Ia ), we approximate the effective number of data points in the DES-SN5YR sample by ∑ P B(Ia) = 1735 (rather than the total number of data points, 1829).  \nDES-SN5Y  \nDES-SN5Y  \nDES-SN5Y  \nDES-SN5Y  \nTable 2. Results for four different cosmological models, sorted into sections for different combinations of observational constraints. These are the medians of the marginalized posterior with 68.27% integrated uncertainties ('cumulative' option in ChainConsumer). For each fit we also show the χ 2 per degree of freedom as a measure of the goodness of fit.  \nIdeally, a good fit should have χ 2 / d.o.f. ∼ 1 . 0. The slightly low χ 2 / d.o.f. for the DES-SN5YR data arises because ∑ P B(Ia) only approximates the number of degrees of freedom, and the same behaviour is also seen in simulations.", '4.2.2. Suspiciousness': "Suspiciousness, S , (Handley & Lemos 2019) is closely related to the Bayes ratio, R , 9 and can be used to assess whether different datasets are consistent. However, while the Bayes ratio has been shown to be priordependent (Handley & Lemos 2019), with wider prior widths boosting the confidence, Suspiciousness is prior independent. Therefore, Suspiciousness is ideal for cases such as ours where we have chosen deliberately wide and uninformative priors (Lemos et al. 2021, Sec. 4.2). Trotta (2008) suggests ln S < -5 is 'strong' tension, -5 < ln S < -2 . 5 is 'moderate' tension, and ln S > -2 . 5 indicates the datasets are in agreement.  \nWe determine ln S using the ANESTHETIC software (Handley 2019), which produces an ensemble of realizations used to estimate sample variance. Results are  \nDES-SN5YR vs CMB  \nFigure 9. Measurements of Suspiciousness (∆ ln( S )) between the DES-SN5YR and Planck 2020 datasets for the four models constrained in this paper. Further left indicates higher tension where the shaded regions reflect 'moderate' (yellow) evidence of tension according to Trotta (2008). The values and uncertainties represent the mean and standard deviation of realizations estimating sample variance using the ANESTHETIC software.  \n<!-- image -->  \nquoted using the mean of the ensemble, with the error bars reflecting the standard deviation.  \nIn Fig. 9 we plot the Suspiciousness values for the DES-SN5YR data vs Planck 2020 and vs BAO+3 × 2pt data. We find no indication of tension using any of the four models investigated in this paper.  \nFigure 10. Bayesian Evidence difference relative to FlatΛCDM (∆(ln BE )). We present the results for the four different models tested in this analysis and for the three combination of datasets used (DES only in cyan, DES+Planck in blue, DES+BAO+3 × 2pt in orange). An increase (decrease) in ∆(ln BE ) indicates that a model is disfavoured (favoured) compared to Flat-ΛCDM.  \n<!-- image -->", '4.3. Model Selection': "Finally, we use Bayesian Evidence to test whether the extra parameters in the more complex models we test are warranted, given the data. In Fig. 10, we present the difference in the logarithm of the Bayesian Evidence, ∆(ln BE ), relative to Flat-ΛCDM for the four different models tested in this analysis and for the three combinations of datasets used in Fig. 10.  \nTo evaluate the strength of evidence when comparing Flat-ΛCDM with more complex models, we again use Jeffreys' scale. This empirical scale suggests that ∆(ln BE ) > 2 . 5 (and < -2 . 5) is moderate evidence against (in support of) the more complex model, whereas ∆(ln BE ) > 5 (and < -5) is strong evidence against (in support of) the more complex model (for a review of model selection in cosmology see Trotta 2008). We note that none of the datasets considered in this analysis strongly favours cosmological models beyond Flat-ΛCDM. The priors that we choose for model comparison are w ∈ ( -1 . 5 , -0 . 5), w a ∈ ( -10 , 10) and Ω K ∈ ( -0 . 5 , 0 . 5). We consider these priors (which determine the penalty for more complex models) to be reasonable in terms of general considerations, such as avoiding universes that are younger than generally accepted stellar ages (see Section 5.1.3). Although our chains have been run on uninformative priors, the Bayesian Evidence from those chains may be adjusted for these harmonized priors as described in Appendix 3.", '5.1.1. Is the expansion of the Universe accelerating?': 'Twenty five years ago Riess et al. (1998) found 99.5%99.9% (2 . 8 σ to 3 . 9 σ ) evidence for an accelerating Universe, by considering the deceleration parameter q ≡ ( a a )˙ a -2 and integrating over the likelihood that q 0 < 0. Importantly they note that since q 0 is measured at the present day but the data span a wide range of redshifts, q 0 can only be measured within the context of a model, either cosmographic or physically motivated. They used the ΛCDM model, in which q 0 = Ω M / 2 -Ω Λ .  \nDoing the same with DES-SN5YR data gives 99.99998% confidence (5 . 2 σ ) that q 0 < 0 in ΛCDM, or a 2 × 10 -7 chance that the expansion of the Universe is not accelerating. As noted in Section 4.1.3, our confidence is even higher that the universe was accelerating at z ∼ 0 . 2. When we further assume flatness, the confidence in an accelerating Universe is overwhelming (no measurable likelihood for a decelerating Universe) and we find q 0 = -0 . 530 +0 . 018 -0 . 017 . For more fits of q 0 using a cosmographic approach see Camilleri et al. (in prep. 2024).', '5.1.2. Is dark energy a cosmological constant?': "As seen in Sec 4.1, a cosmological constant is a good fit to our data, but not the best fit. Our best fit equation of state parameter is slightly (more than 1 σ ) higher than the cosmological constant value of w = -1 (both for SNe alone and in combination with Planck or BAO+3 × 2pt). Our result agrees with the recent result from the UNION3 compilation analyzed with the UNITY framework (Rubin et al. 2023) (which appeared while this paper was under internal review). The Pantheon+ result (Brout et al. 2022a) is within 1 σ of w = -1, but also on the high side ( w = -0 . 90 ± 0 . 14).  \nFurthermore, our analysis slightly prefers a timevarying dark energy equation of state parameter when we fit for w ( a ) such that the equation of state parameter increases with time (again for all data combinations), known as a 'thawing' model. Model selection, however, is inconclusive.  \nThe constraints on time-varying w are enabled by the wide redshift range of the DES-SN5YR sample. Our analysis as described in Vincenzi et al. (2024) gives us confidence that systematic uncertainties in this data are below the level of our statistical precision. Nevertheless, it is important to recognize that (a) the lowz sample is the one for which we have the least systematic control and (b) the very high-redshift SNe are the ones for which bias-corrections are large ( > 0 . 1 mag) and more uncertain (e.g., accurate estimation of spectroscopic redshift efficiency is more challenging as we go to higher red-  \nshifts), and for which the uncertainties on the rest-frame UV part of the SN Ia spectral energy distribution have more impact on SN distances estimations (see also Brout et al. 2022a).  \nTo test whether our fits are dominated by any particular redshift range we ran cosmological fits (a) removing lowz data (i.e., DES SNe alone) and (b) removing highz data (i.e., removing ∼ 80 SNe at z > 0 . 85, for which we use only two bands; see Fig. 2). Most of the cosmological results obtained with the subsamples are consistent with the results found for the full sample. However, we found that removing the lowz sample shifts the contours in the Flatw CDM slightly down, which would make the combined fits more consistent with w = -1. The Flatw 0 w a CDM results are stable to sub-sample selection. See Appendix C for details.  \nWe showed in Vincenzi et al. (2024) that systematic uncertainties are sub-dominant to the statistical uncertainties in our sample. Nevertheless, in the future a new low-redshift sample (see Sec. 5.3) would help alleviate any remaining doubt about calibration and systematics in the existing lowz sample, and an even higher-redshift supernova survey would help alleviate any modelling concerns by minimizing selection effects even at z ∼ 1.", '5.1.3. How old is the Universe?': "One of the issues that the discovery of dark energy solved is the age of the Universe ( t 0 ) problem - globular cluster age estimates, in combination with high estimates of H 0 , were inconsistent with models that were not accelerating (VandenBerg et al. 1996; Gratton et al. 1997; Chaboyer et al. 1998).  \nOur results, which favor a dark energy equation of state parameter slightly higher than w = -1 would imply that the age is slightly younger than the age found in a Universe where dark energy is a cosmological constant (for the same values of H 0 and present dark energy density).  \nTo calculate the Universe's age, one needs a value of H 0 in addition to the best fit cosmological model. Since we do not constrain H 0 in this analysis, we present our measurement of the combination H 0 t 0 . In other words, we give t 0 in units of the Hubble time t H ≡ 1 /H 0 . 10 Our best-fit DES-SN5YR result in Flat-ΛCDM would have an age of (0 . 921 ± 0 . 013) t H . This is ∼ 3% younger than Planck ( t Planck age = (0 . 950 ± 0 . 007) t H ), corresponding to an age difference of approximately -0 . 4 Gyr. Our best fit Flatw 0 w a CDM model gives an age (0 . 86 ± 0 . 02) t H , about 9% younger than the Flat-ΛCDM Planck result,  \ncorresponding to an age difference of approximately -1 . 3 Gyr. Such a young age is unlikely given the age of the oldest globular clusters (Valcin et al. 2020; Cimatti & Moresco 2023; Ying et al. 2023). In the future, this information could be used as a prior to limit the feasible range of time-varying dark energy.", '5.1.4. Does our best fit resolve the Hubble tension?': 'As pointed out in Planck Collaboration (2020, their Sec. 5.4), the only basic extensions to the base FlatΛCDM model that resolve the H 0 tension are those in which the dark energy equation of state is allowed to vary away from w = -1. In the w CDM model a phantom equation of state parameter of w ∼ -1 . 5 would help resolve the tension (Di Valentino et al. 2021, their Sec. 5.1), and it is clear from Fig. 7 that CMB alone actually prefers w < -1. In this model, Planck alone does not constrain H 0 very tightly, and they refrain from quoting a value, (see Table 5 of Planck Collaboration (2020)), but lower w correlates with higher H 0 . However, the DES-SN5YR data shows a slight tendency for w > -1, essentially ruling out this solution within w CDM.', '5.2. Comparison with DES-SN3YR and Pantheon+': "It is informative to compare the results of the previous DES-SN3YR analysis (Dark Energy Survey Collaboration 2019; Brout et al. 2019a) with the results of the DES-SN5YR analysis presented in this work. The DES-SN3YR analysis included 207 spectroscopically confirmed SNe Ia from DES and 127 low-redshift SNe from CfA and CSP samples (see also Fig. 3). A fraction of those events is in common between both analyses (55 from lowz external samples and 146 DES SNe). 11  \nHowever, the DES-SN3YR analysis differs from the analysis presented here in many aspects. The SN Ia intrinsic scatter modelling has been significantly improved (from 'G10' and constant σ int floor, to the more sophisticated modelling of intrinsic scatter introduced by Brout & Scolnic 2021; Popovic et al. 2023a), the BBC software has been updated (from BBC '5D' and a binned approach, to BBC '4D' and an unbinned approach), the x 1 -M ⋆ correlations have been incorporated into simulations (following the work by Smith et al.  \nFigure 11. Comparison between Hubble residuals for the DES-SN3YR and DES-SN5YR analyses w.r.t. the best fit Flatw CDM for the DES-SN5YR analysis. Hubble residuals are binned in redshift and we present the weighted mean and standard deviation of the mean in each redshift bin. The redshift range covered by the lowz sample is highlighted and shown with thick dotted lines. The two DES samples are consistent with each other. Note the DES-SN3YR analysis only includes spectroscopically confirmed SNe whereas the DES sample in the DES-SN5YR analysis consists entirely of photometrically identified SNe Ia and extends to higherz .  \n<!-- image -->  \n2020b; Popovic et al. 2021), and the light-curve fitting model has been updated from the SALT2 model to the SALT3 model (see Taylor et al. 2023, for a comparison between SALT2 and SALT3 using the DES-SN3YR sample). Finally, the DES-SN3YR analysis did not require machine-learning classification and the implementation of the BEAMS approach because it is a sample of spectroscopically selected SNe Ia. We compare the final SN distances in Fig. 11 and find consistent results (differences in binned distances are on average 0.02 mag, even in the redshift ranges where contamination is expected to be high). The cosmological results from DES-SN3YR and DES-SN5YR are consistent within uncertainties (when assuming Flat-ΛCDM, Ω M are 0 . 331 ± 0 . 038 and 0 . 352 ± 0 . 017 for DES-SN3YR and DES-SN5YR respectively, while when assuming Flatw CDM and including CMB priors, w are -0 . 978 ± 0 . 059 and -0 . 955 +0 . 032 -0 . 037 ).  \nThe other main dataset we can compare to is Pantheon+, which contains a significant amount of independent data (all the highz data). The DES sample is on average much higher redshift than the Pantheon+ sample (see Fig. 3), with over a quarter of the DES-SN5YR sample being at high enough redshift ( z ≳ 0 . 64) to probe the likely decelerating 12 period of the Universe (compared to 6% in Pantheon+). We show a comparison of the contours in Fig. 12. We find very similar constrain-  \nFigure 12. Constraints in Flatw CDM from the DESSN5YR sample, the Pantheon+ sample (with and without CMB priors), and the Amalgame sample. The constraining power of the DES-SN5YR and Pantheon+ samples is comparable and consistent, despite Pantheon+ being a spectroscopic SN Ia sample combining 17 different surveys. The 'Amalgame' sample includes the SDSS and PS1 photometric SN samples ( > 1700 intermediate-redshift and high-redshift SNe), however it does not include a lowz anchoring sample (hence the larger contours). DES-SN5YR and Pantheon+ are also combined with CMB constraints (for both we use the Planck lite Python implementation presented by Prince &Dunkley 2019). The horizontal dotted line marks the equation of state values for a cosmological constant.  \n<!-- image -->  \ng power between Pantheon+ and DES-SN5YR, and the DES-SN5YR value of w is within 1 σ of Pantheon+ (Brout et al. 2022a). These analyses are not fully independent as a fraction of the lowz sample is shared. However, all of the highz dataset is independent, and DES is a photometric sample while Pantheon+ is fully spectroscopic. The constraints on w are similar between DES and Pantheon+ as DES highz has better precision per SN than Pantheon+ and has significantly higher statistical power at z > 0 . 4 (see Fig. 3), but Pantheon+ used 2 × more low-redshift SNe (which we do not include in order to be able to better control systematic uncertainties).", '5.3. DES and Next Generation Supernova Samples': "This analysis has shown that moving from a spectroscopically confirmed sample as done in Dark Energy Survey Collaboration (2019) to a photometric sample can increase the sample size of well-measured supernovae  \nsignificantly (from 207 DES SNe Ia in DES-SN3YR to > 1600 in DES-5YR), consistent with an analysis of Pan-STARRS SNe in Jones et al. (2018). This improvement arises because photometric classification alleviates the bottleneck of limited spectroscopic resources. The improvement will increase for future surveys as more candidates are discovered, but the available time for spectroscopy does not increase commensurately. Importantly, the work of Vincenzi et al. (2024) shows that systematic uncertainties due to photometric classification are not limiting. Instead, the 'conventional' systematics of calibration and modeling the intrinsic scatter remain the most significant challenges.  \nThere is potential for further increase of the statistical power of the DES sample if one moves to using SNe in which a host galaxy spectroscopic redshift was not acquired and instead relies on photometric redshifts of the SNe and the galaxy. This path was explored by Chen et al. (2022) for a subset of DES SNe, namely ones that occur in redMaGiC galaxies, and has been explored as well for SuperNova Legacy Survey (SNLS, Ruhlmann-Kleider et al. 2022) and the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) in Mitra et al. (2023). These analyses show that the use of photoz s do not introduce systematic uncertainties to a scale similar to the statistical uncertainties. This potential is highlighted by the ≈ 2400 SNe Ia identified without host galaxy spectroscopic redshift in DES that could be used for this type of analysis (Moller & the DES Collaboration in prep. 2024).  \nThe DES supernova survey was supported by the 6year OzDES survey on the Anglo-Australian Telescope (described in Lidman et al. 2020), which took multifibre observations of host galaxies to acquire redshifts of host galaxies of SNe. The total investment of this program was 100 nights, and for roughly 75% of the targeted host galaxies a spectroscopic redshift has been secured. This program was fortuitous as the cameras for OzDES and DECam have a nearly identical field-ofview. Enormous resources would be needed to reproduce this joint program for LSST, which will find millions of SNe across 18,000 square degrees (Ivezi'c et al. 2019; S'anchez et al. 2022) (compared to the 27 square degrees of DES SNe). Surveys such as 4MOST will follow-up tens of thousands of these (Swann et al. 2019), but the full wealth of transient information may benefit from an entirely photometric approach.  \nAs statistical precision continues to improve thanks to the increased number of supernovae, a main theme for systematic analysis is second-order relations between different systematics. Typically, systematics are treated independently when building the covariance matrix. We  \nhave implemented a method to account for calibration systematics along with light-curve model systematics together, but this is currently the only joint exercise. This type of work will grow in importance. For example, while photometric classification does not directly cause a large increase in the error budget, it hinders the ability to constrain the intrinsic scatter model preferred by the data. Potentially, if LSST and other surveys such as those enabled by the Nancy Grace Roman Space Telescope have enough supernovae (Rose et al. 2021), the dataset can enable a forward modeling approach such as the Approximate Bayesian Computation method introduced in Jennings et al. (2016) and worked on in Armstrong et al. (in prep), which could vary all systematics, nuisance, and cosmological parameters at the same time to compare against the data.  \nFurthermore, as discussed in Section 5.1.2, modeling of the lowz sample remains a source of systematic uncertainty. This sample comes from a multitude of surveys, even though we have removed many of the older inhomogeneous sources compared to analyses like Pantheon+. In the near future, we expect additions from Zwicky Transient Factory (Smith et al. in prep. 2024), Young Supernova Experiment (Jones et al. 2021; Aleo et al. 2023), and Dark Energy Bedrock All-sky Supernova Survey (DEBASS, PI: Brout) to improve lowz constraints of the SN Hubble Diagram, given their improved calibration and better understood selection function. 13 DEBASS will be particularly fruitful as it is a low-redshift sample taken with DECam, so a single instrument and calibration catalog will be used for the full sample of DEBASS+DES, similar to the singleinstrument PS1 sample in Jones et al. (2019). Using simulations, we estimate that quadrupling the size of our lowz sample (from ∼ 200 to ∼ 800 SNe expected from this next generation of lowz SN surveys) could enable a reduction of uncertainties on w by ∼ 30 per cent (for a Flat w CDM model, using SN data alone).  \nLastly, we note that while LSST and Roman may help improve a number of these issues, the first data release is still > 3 years away. We encourage work with the DES-SN sample as presented here, combined with other samples. Popovic et al. (2023b) recently showed the ability to combine separate photometric samples (PS1 and SDSS) into the Amalgame sample (also shown in Fig. 12, and a similar analysis can be done by combining DES with these. It is reasonable to expect that with new low-redshift samples, and combination of high-redshift  \nphotometric samples, a sample with > 5000 likely SNe Ia can be compiled in the very near future.", '6. CONCLUSIONS': "The DES Supernova survey stands as a groundbreaking milestone in SN cosmology. With a single survey, we effectively tripled the number of observed SNe Ia at z > 0 . 2 and quintupled the number beyond z > 0 . 5. Here we present the unblinded cosmological results, and in companion papers make public the calibrated light curves and Hubble diagram from the full sample of DES Type Ia supernovae (S'anchez in prep. 2024; Vincenzi et al. 2024).  \nAfter combining the 1635 DES SNe (of which 1499 have a probability > 0 . 5 of being a SN Ia) with 194 existing lowz SNe Ia, we present final cosmological results for four variants on ΛCDM cosmology, as summarized in Table 2.  \nThe standard Flat-ΛCDM cosmological model is a good fit to our data. When fitting DES-SN5YR alone and allowing for a time-varying dark energy we do see a slight preference for a dark energy equation of state that becomes greater (closer to zero) with time ( w a < 0) but this is only at the ∼ 2 σ level, and Bayesian Evidence ratios do not strongly prefer the Flatw 0 w a CDM cosmology.  \nWe compare cosmological results from each of our models to results from the CMB analysis of Planck Collaboration (2020). There are some differences in the best fit values but in each case we find consistency to within 2 σ and a Suspiciousness statistic that indicates agreement among the datasets.  \nCritically, the DES-SN5YR analysis shown here demonstrates that contamination due to SN classification and host-galaxy matching is not a limiting systematic for SN cosmology; this opens the path for a new era of cosmological measurements using SN samples that are not limited by live spectroscopic follow-up of SNe. Instead, our analysis shows the SN community that there are other factors that will be crucial for the success of future SN experiments: a high-quality low-redshift sample, a robust UV and NIR extension of light-curve fitting models, excellent control of selection effects across the entire redshift range, and improvement in our understanding of SN Ia intrinsic scatter properties and the role played by interstellar dust.  \nFuture work will conclude the Dark Energy Survey by combining these supernova results with the other three pillars of DES cosmology, namely baryon acoustic oscillations, galaxy clustering, and weak lensing.", 'ACKNOWLEDGMENTS': "We acknowledge the following former collaborators, who have contributed directly to this work - Ricard Casas, Pete Challis, Michael Childress, Ricardo Covarrubias, Chris D'Andrea, Alex Filippenko, David Finley, John Fisher, Francisco Forster, Daniel Goldstein, Santiago Gonz'alez-Gait'an, Ravi Gupta, Mario Hamuy, Steve Kuhlmann, James Lasker, Marisa March, John Marriner, Eric Morganson, Jennifer Mosher, Elizabeth Swann, Rollin Thomas, and Rachel Wolf.  \nT.M.D., A.C., R.C., S.H., acknowledge the support of an Australian Research Council Australian Laureate Fellowship (FL180100168) funded by the Australian Government, and A.M. is supported by the ARC Discovery Early Career Researcher Award (DECRA) project number DE230100055. M.S., H.Q., and J.L are supported by DOE grant DE-FOA-0002424 and NSF grant AST-2108094. R.K. is supported by DOE grant DE-SC0009924. M.V. was partly supported by NASA through the NASA Hubble Fellowship grant HST-HF2-51546.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. L.K. thanks the UKRI Future Leaders Fellowship for support through the grant MR/T01881X/1. L.G. acknowledges financial support from the Spanish Ministerio de Ciencia e Innovaci'on (MCIN), the Agencia Estatal de Investigaci'on (AEI) 10.13039/501100011033, and the European Social Fund (ESF) 'Investing in your future' under the 2019 Ram'on y Cajal program RYC2019-027683-I and the PID2020-115253GAI00 HOSTFLOWS project, from Centro Superior de Investigaciones Cient'ıficas (CSIC) under the PIE project 20215AT016, and the program Unidad de Excelencia Mar'ıa de Maeztu CEX2020001058-M, and from the Departament de Recerca i Universitats de la Generalitat de Catalunya through the 2021-SGR-01270 grant. R.J.F. and D.S. were supported in part by NASA grant 14-WPS14-0048. The UCSC team is supported in part by NASA grants NNG16PJ34G and NNG17PX03C issued through the Roman Science Investigation Teams Program; NSF grants AST1518052 and AST-1815935; NASA through grant No. AR-14296 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation; and fellowships from the Alfred P. Sloan Foundation and the David and Lucile Packard Foundation to R.J.F. We acknowledge the University of Chicago's Research Computing Center for their support of this work.  \nFunding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and AstroParticle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Funda¸c˜ao Carlos Chagas Filho de Amparo 'a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cient'ıfico e Tecnol'ogico and the Minist'erio da Ciˆencia, Tecnologia e Inova¸c˜ao, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey.  \nThe Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energ'eticas, Medioambientales y Tecnol'ogicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ci'encies de l'Espai (IEEC/CSIC), the Institut de F'ısica d'Altes Energies, Lawrence  \nBerkeley National Laboratory, the Ludwig-Maximilians Universitat Munchen and the associated Excellence Cluster Universe, the University of Michigan, NSF's NOIRLab, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas A&M University, and the OzDES Membership Consortium.  \nBased in part on observations at Cerro Tololo Inter-American Observatory at NSF's NOIRLab (NOIRLab Prop. ID 2012B0001; PI: J. Frieman), which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. Based in part on data acquired at the Anglo-Australian Telescope. We acknowledge the traditional custodians of the land on which the AAT stands, the Gamilaraay people, and pay our respects to elders past and present. Parts of this research were supported by the Australian Research Council, through project numbers CE110001020, FL180100168 and DE230100055. Based in part on observations obtained at the international Gemini Observatory, a program of NSF's NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini Observatory partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigaci'on y Desarrollo (Chile), Ministerio de Ciencia, Tecnolog'ıa e Innovaci'on (Argentina), Minist'erio da Ciˆencia, Tecnologia, Inova¸c˜oes e Comunica¸c˜oes (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). This includes data from programs (GN-2015B-Q-10, GN2016B-LP-10, GN-2017B-LP-10, GS-2013B-Q-45, GS-2015B-Q-7, GS-2016B-LP-10, GS-2016B-Q-41, and GS-2017B-LP-10; PI Foley). Some of the data presented herein were obtained at Keck Observatory, which is a private 501(c)3 non-profit organization operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration (PIs Foley, Kirshner, and Nugent). The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. This paper includes results based on data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile (PI Foley), and the Southern African Large Telescope (SALT) (PIs M. Smith & E. Kasai). The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the Native Hawaiian  \ncommunity. We are most fortunate to have the opportunity to conduct observations from this mountain.  \nThe DES data management system is supported by the National Science Foundation under Grant Numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MICINN under grants ESP2017-89838, PGC2018-094773, PGC2018-102021, SEV-2016-0588, SEV-20160597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Program (FP7/2007-2013) including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Brazilian Instituto Nacional de Ciˆencia e Tecnologia (INCT) do e-Universo (CNPq grant 465376/2014-2).  \nThis research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC0205CH11231 using NERSC award HEP-ERCAP0023923. This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.  \nFacilities: CTIO:4m, AAT, Gemini:Gillett (GMOSN), Gemini:South (GMOS-S), Keck:I (LRIS), Keck:II (DEIMOS), Magellan:Baade (IMACS), Magellan:Clay (LDSS3, MagE), SALT  \nSoftware: numpy (Harris et al. 2020), astropy (Astropy Collaboration 2013, 2018), matplotlib (Hunter 2007), pandas (Pandas development team 2020), scipy (Virtanen et al. 2020), SNANA (Kessler et al. 2009), Pippin (Hinton & Brout 2020), ChainConsumer (Hinton 2016), Source Extractor (Bertin & Arnouts 1996), MINUIT (James & Roos 1975), SuperNNova (Moller & de Boissi'ere 2020), SCONE (Qu et al. 2021).", 'A. DATA RELEASE AND HOW TO USE THE DES-SN5YR DATA': "Here we explain where to find the data and software necessary to reproduce our analysis. Many of the codes we use are already public (detailed below). The key data, code, and tutorials are available on Github at https: //github.com/des-science/DES-SN5YR.  \nThe DES-SN5YR analysis was run using the pippin pipeline framework (Hinton & Brout 2020) 14 that orchestrated SNANA codes for simulations, light curve fitting, BBC, and covariance matrix computation ( SNANA , Kessler et al. 2009), 15 and also integrated photometric classification from Moller & de Boissi'ere (2020) 16 and Qu et al. (2021). 17 Additional analyses codes that run outside the main pipeline include Scene Model Photometry (Brout et al. 2019b), fit  \nto measure the SN population of stretch and color (Popovic et al. 2023a), 18 SALT3 training (Kenworthy et al. 2021), 19 and CosmoSIS to fit for cosmological parameters (Zuntz et al. 2015). 20  \nWe release the pippin input files necessary to (i) generate and fit all the simulations used in the analysis (both the large 'biasCor' simulations to calculate bias corrections, and the DES-SN5YR-like simulated samples to validate the analysis); (ii) reproduce the full cosmological analysis, from light-curve fitting to photometric classification, distance estimates and cosmological fitting. Auxiliary files are also available within the SNANA library. 21  \nThe various (intermediate and final) outputs of our analysis pipeline are also provided. This includes (i) light-curve fitted parameters, (ii) light-curve classification results, (iii) the final Hubble diagram and associated uncertainties covariance matrices, and (iv) the cosmology chains.", 'B. PRIORS': "Table 3 lists the prior ranges for our MCMC chains. The priors related to external data sets align with the priors in the original papers. We adapted the prior ranges to enclose the majority of the high likelihood region as appropriate for each data set and model combination. Data-set specific priors are listed in the footnote to the table.  \nBayesian Evidence calculations depend on the choice of prior; larger prior ranges used on the same data and likelihoods lead to lower evidences, sometimes referred to as the complex model penalty . Therefore in model comparison using evidence calculations, we took care to choose consistent prior ranges that do not unduly inflate this penalty. Bayes' Theorem states,  \np ( M | D ) = p ( D | M ) p ( M ) p ( D ) ∝ p ( D | M ) , (B1)  \nwhere D is the data and M is the model, and the proportionality to the Bayesian Evidence p ( D | M ) follows from assuming no prior preference for any model. Writing the model parameters as ⃗ θ we can then write,  \np ( D | M ) = ∫ p ( D, ⃗ θ | M ) d N θ = ∫ p ( D | ⃗ θ, M ) p ( ⃗ θ ) d N θ = p ( ⃗ θ ) ∫ p ( D | ⃗ θ, M ) d N θ , (B2)  \nwhere the last step assumes a constant prior for each of the N parameters θ i of model M , that fully encompasses the support of the likelihood function (this is true to a very good approximation for the models that are tested here). Making explicit the dependence of the Bayesian Evidence on the model prior by writing p ( D | M ) = BE ( ⃗ θ ), the evidence may then be adjusted for a change in prior volume without recomputing the chains as follows :  \nln BE ( ⃗ θ 2 ) = ln BE ( ⃗ θ 1 ) + ln p ( ⃗ θ 1 ) -ln p ( ⃗ θ 2 ) , (B3)  \nwhere using ( θ i, min , θ i, max ) for the prior range for each parameter,  \np ( ⃗ θ ) = N ∏ i =1 1 θ i, max -θ i, min . (B4)", 'C. TESTS ON SUBSETS OF OUR DATA': 'The large redshift range of the DES-SN5YR sample provides a strong lever arm on the measurement of any time variation of dark energy. We therefore check for potential peculiarities at the extremes of our redshift range that are driving the fit toward non-cosmological-constant values.  \nIn Fig. 13 and Table 4, we show the change to the Flat-ΛCDM, Flatw CDM and Flatw 0 w a CDM fits using DES-SN alone (no Lowz external samples) and when using the full DES-SN5YR sample but excluding the highest redshift SNe ( z > 0 . 85, the 5 per cent highest redshift events in our DES SN sample). We show, for example, that in FlatΛCDM excluding the Lowz sample lowers the best fit value to Ω noLow -z M =0 . 330 ± 0 . 024 (∆Ω M = -0 . 022), which closer agreement with the CMB value of Ω Planck M =0 . 317 ± 0 . 008. Similarly, excluding high redshift SNe lowers the best fit value to Ω noHigh -z M =0 . 342 ± 0 . 017 (∆Ω M = -0 . 010). However, it is important to quantify the significance of the observed shifts.  \nTable 3. Priors §  \n<!-- image -->  \nFigure 13. Constraints for the full DES-SN5YR dataset (cyan), when excluding lowz SNe ( z < 0 . 1, grey dashed line), and when excluding highz SNe ( z > 0 . 85, brown dotted-dash line). In Flatw CDM (left) the contours shift primarily along the degeneracy line (and in opposite directions for the lowz and highz cuts), but also slightly perpendicular to the degeneracy direction. In combination with the CMB prior this pushes the result closer to w = -1 in the no-lowz case. The Flatw 0 w a CDM model (right) best fit sees no significant shifts with sub-sample selection.  \n<!-- image -->  \nThe cosmological contours using the full DES-SN5YR sample, the DES-SN5YR sample without Lowz , and the DES-SN5YR sample without Highz cannot be directly compared as if they were three independent measurements (the three datasets used have large overlaps). Therefore, in order to examine the significance of the observed shifts, we generate 100 independent realizations of the DES-SN5YR Hubble diagram applying the Cholesky Decomposition to the full DES-SN5YR data vector of 1829 SNe, and the associated 1829 × 1829 statistical and systematic covariance matrix. For each independent realization, we fit the cosmological parameters with and without the Lowz and Highz samples and estimate the standard deviation ( σ ) of the estimated ∆Ω M (or ∆ w and/or ∆ w 0 and ∆ w a when fitting for Flatw CDM and Flatw 0 w a CDM). Using this approach, we measure a σ (∆Ω M ) of 0.02 and 0.005 when fitting for Flat-ΛCDM and excluding Lowz and Highz SNe respectively, and we conclude that the ∆Ω M observed on the real data are significant at the 1 . 1 σ and 2 . 1 σ respectively.  \nIn Flatw CDM, excluding Lowz gives a best fit w = -1 . 34 ± 0 . 32 (∆ w =0 . 54) and excluding Highz gives a best fit w = -0 . 66 ± 0 . 11 (∆ w = -0 . 14). Using our 100 realizations with systematics, we estimate that the significance of the shifts is 2 . 3 σ and -2 . 2 σ , respectively.  \nWe perform the same test incorporating a CMB-like prior. Estimating the best-fit Flatw CDM from our SN subsamples combined with the full CMB likelihood from Planck Collaboration (2020) is computationally expensive and practically unfeasible for data and 100 simulations. For this reason, we use an approximation of a CMB-like prior that uses the R -parameter (defined, e.g., in Komatsu et al. 2009, see Eq. 69) from Planck Collaboration (2020). This CMB-prior approximation is incorporated in the fast minimization cosmological fitting program wfit , available in SNANA. When combining SNe and the approximated CMB prior and fitting for Flatw CDM, we find that the shifts observed in w are not statistically significant (less than 2 σ ).  \nWe make similar tests for Flatw 0 w a CDM model. The main results are consistent for the different redshift cuts, with the central value varying less than the Flatw CDM case despite (or because of) the extra flexibility of Flatw 0 w a CDM. If not statistical fluctuations, the observed shifts in w when removing either low or highz SNe would be expected if the Flatw CDM model is inadequate and cannot simultaneously fit the both low and high redshift range in our data; but it is also what you expect if there is some kind of systematic error in the lowz or highz data. Future independent data sets (both supernovae and other measures of expansion such as Baryon Acoustic Oscillations) are essential to  \nTable 4. Results using DES data alone (excluding Lowz below z < 0 . 1) and DES-SN5YR without highz SNe ( z < 0 . 85). Shift significance: the significance of shifts in either Ω M (when fitting for FlatΛCDM model) or w (when testing Flat w CDM) is estimated from 100 simulations.  \ndetermine which is the better explanation. The seemingly large values of some of the shifts in cosmological parameters are due to the strong degeneracy in the w -Ω M plane, as seen in Fig. 13. Once combined with external data, such as a CMB prior, it is more evident that the shift perpendicular to the degeneracy direction is small (e.g. line 3 of Table 4).', 'REFERENCES': '```\nAlam, S., Ata, M., Bailey, S., et al. 2017, MNRAS, 470, 2617 Alam, S., Aubert, M., Avila, S., et al. 2021, PhRvD, 103, 083533 Alard, C. & Lupton, R. H. 1998, ApJ, 503, 325 Aleo, P. D., Malanchev, K., Sharief, S., et al. 2023, ApJS, 266, 9 Armstrong, P., Qu, H., Brout, D., et al. 2023, PASA, 40, e038 Astropy Collaboration. 2013, A&A, 558, A33 Astropy Collaboration. 2018, AJ, 156, 123 Bautista, J. E., Paviot, R., Vargas Maga˜na, M., et al. 2021, MNRAS, 500, 736 Bernstein, J. P., Kessler, R., Kuhlmann, S., et al. 2012, ApJ, 753, 152 Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393 Betoule, M., Kessler, R., Guy, J., et al. 2014, A&A, 568, A22 Blanton, M. R., Bershady, M. A., Abolfathi, B., et al. 2017, AJ, 154, 28 Brout, D., Hinton, S. R., & Scolnic, D. 2021, ApJL, 912, L26 Brout, D. & Scolnic, D. 2021, ApJ, 909, 26 Brout, D., Scolnic, D., Kessler, R., et al. 2019a, ApJ, 874, 150 Brout, D., Sako, M., Scolnic, D., et al. 2019b, ApJ, 874, 106 Brout, D., Scolnic, D., Popovic, B., et al. 2022a, ApJ, 938, 110 Brout, D., Taylor, G., Scolnic, D., et al. 2022b, ApJ, 938, 111 Burke, D. L., Rykoff, E. S., Allam, S., et al. 2018, AJ, 155, 41 Camilleri, R., Davis, T., & the DES Collaboration. in prep. 2024 Chaboyer, B., Demarque, P., Kernan, P. J., & Krauss, L. M. 1998, ApJ, 494, 96 Chen, R. et al. 2022, ApJ, 938, 62 Chen, R., Scolnic, D., Rozo, E., et al. 2022, ApJ, 938, 62 Chevallier, M. & Polarski, D. 2001, IJMP D, 10, 213 Childress, M. J., Lidman, C., Davis, T. M., et al. 2017, MNRAS, 472, 273 Cimatti, A. & Moresco, M. 2023, ApJ, 953, 149 Conley, A., Guy, J., Sullivan, M., et al. 2011, ApJS, 192, 1 Dark Energy Survey Collaboration. 2016, MNRAS, 460, 1270 Dark Energy Survey Collaboration. 2019, ApJL, 872, L30 Dark Energy Survey Collaboration. 2022, PhRvD, 105, 023520 Dark Energy Survey Collaboration. 2023, PhRvD, 107, 083504\n```  \n```\nWiseman, P., Sullivan, M., Smith, M., et al. 2021, MNRAS, 506, 3330 Wiseman, P., Vincenzi, M., Sullivan, M., et al. 2022, MNRAS, 515, 4587 Ying, J. M., Chaboyer, B., Boudreaux, E. M., et al. 2023, AJ, 166, 18\n```  \n```\nYuan, F., Lidman, C., Davis, T. M., et al. 2015, MNRAS, 452, 3047 Zuntz, J., Paterno, M., Jennings, E., et al. 2015, Astronomy and Computing, 12, 45\n```'}