Recent results from the Dark Energy Spectroscopic Instrument DESI collaboration have been interpreted as evidence for evolving dark energy. However this interpretation is strongly dependent on which Type Ia supernova SN sample is combined with DESI measurements of baryon acoustic oscillations BAO and observations of the cosmic microwave background CMB radiation. The strength of the evidence for evolving dark energy ranges from 3.9 sigma for the Dark Energy 5 year DES5Y SN sample to  2.5 sigma for the Pantheon sample. Here I compare SN common to both the DES5Y and Pantheon compilations finding evidence for an offset of 0.04 mag. between low and high redshifts. Correcting for this offset brings the DES5Y sample into very good agreement with the Planck LCDM cosmology. Given that most of the parameter range favoured by the uncorrected DES5Y sample is discrepant with many other cosmological datasets I conclude that the evidence for evolving dark energy is most likely a result of systematics in the DES5Y sample.
['Astrophysics - Cosmology and Nongalactic Astrophysics']
Evolving Dark Energy or Supernovae Systematics
{'George Efstathiou': 'Kavli Institute for Cosmology Cambridge and Institute of Astronomy, Madingley Road, Cambridge, CB3 OHA.  \n18 October 2024', 'ABSTRACT': 'Recent results from the Dark Energy Spectroscopic Instrument (DESI) collaboration have been interpreted as evidence for evolving dark energy. However, this interpretation is strongly dependent on which Type Ia supernova (SN) sample is combined with DESI measurements of baryon acoustic oscillations (BAO) and observations of the cosmic microwave background (CMB) radiation. The strength of the evidence for evolving dark energy ranges from ∼ 3 . 9 σ for the Dark Energy 5 year (DES5Y) SN sample to ∼ 2 . 5 σ for the Pantheon+ sample. Here I compare SN common to both the DES5Y and Pantheon+ compilations finding evidence for an offset of ∼ 0 . 04 mag. between low and high redshifts. Correcting for this offset brings the DES5Y sample into very good agreement with the Planck ΛCDM cosmology. Given that most of the parameter range favoured by the uncorrected DES5Y sample is discrepant with many other cosmological datasets, I conclude that the evidence for evolving dark energy is most likely a result of systematics in the DES5Y sample.  \nKey words: cosmology: cosmological parameters, dark energy, supernovae', '1 INTRODUCTION': "The nature of dark energy remains an enigma following the discovery of the accelerating Universe over 25 years ago (Riess et al. 1998; Perlmutter et al. 1999). The simplest form of dark energy is a cosmological constant with equation-ofstate w = p/ρc 2 = -1 (see e.g. the review by Weinberg 1989). However, the quantum consequences of eternal deSitter space lead to deep paradoxes suggesting that dark energy is more complicated than a classical cosmological constant (Dyson et al. 2002). One possibility is that our vaccum is metastable, with a lifetime that is much longer than a Hubble time. From the observational point of view, this proposal is indistinguishable from a cosmological constant. An alternative possibility is that the dark energy involves scalar fields and is dynamical (for a comprehensive review see Copeland et al. 2006). In such scenarios, the equationof-state can vary as a function of time, offering an intriguing challenge to observational cosmologists to detect, or set limits, on such a variation.  \nHowever, it is extremely difficult to detect a time variation in w . In the case of a constant w , the observational constraints are extremely tight. For example, the 2018 Planck analysis (Planck Collaboration et al. 2020) found w = -1 . 028 ± 0 . 031 by combining Planck CMB data, baryon acoustic oscillation (BAO) measurements and the Pantheon SN catalogue (Scolnic et al. 2018). The recent paper by the DESI team (DESI Collaboration et al. 2024c, hereafter DESI24) combines Planck CMB data with BAO constraints from the first year DESI observations (DESI Collaboration  \net al. 2024a,b) and the updated Pantheon+ SN catalogue (Scolnic et al. 2022) to infer w = -0 . 997 ± 0 . 025. Despite the differences in the data, the results from these two analyses are consistent and in excellent agreement with the ΛCDM expectation of w = -1.  \nThe situation is very different if w is allowed to vary with time. DESI24 parameterize the evolution of the equation-of-state with redshift z as  \nw ( z ) = w 0 + w a ( z 1 + z ) , (1)  \n(Chevallier & Polarski 2001; Linder 2003) introducing two additional parameters w 0 and w a compared to ΛCDM. It is extremely difficult to disentangle these two parameters. The CMB power spectra show a strong geometrical degeneracy between w a and w 0 along lines of constant angular diameter distance to the last scattering surface (see e.g. Fig. 30 of Planck Collaboration et al. 2020) stratified by either Ω m or H 0 (see e.g. Fig. 6 of Efstathiou (2024)). The CMB power spectra cannot provide strong constraints on evolving dark energy because they are insensitive to departures from the ΛCDM expansion history at low redshift. The BAO data span a redshift range which is too high to measure directly the effects of evolving dark energy favoured by the DES5Y SN data (which as we will see below deviates from the background expansion rate at z < ∼ 0 . 2) In fact, BAO measurements over the redshift range 0 . 3 -2 . 5, including the new DESI BAO measurements, are consistent with the ΛCDM cosmology (e.g. Alam et al. 2017; Planck Collaboration et al. 2020; Alam et al. 2021; DESI Collaboration et al. 2024c).  \nBAO measurements therefore affect inferences on low redshift variations in w indirectly by imposing a constraint on Ω m . Direct inference on variations in w at low redshift is therefore strongly reliant on the magnitude-redshift relation of Type Ia SN.  \nType Ia SN are inherently complex objects. However, heroic efforts over many years have led to 'standardized' SN compilations that have been used extensively to test cosmology. The 2018 Planck papers adopted the Pantheon SN sample (Scolnic et al. 2018) superceeding the earlier SNLS (Conley et al. 2011), Union2.1 (Suzuki et al. 2012) and JLA (Betoule et al. 2014) compilations. DESI24 used three SN catalogues in their analysis of cosmological parameters: the Pantheon+ sample of Scolnic et al. (2022), the Union3 compilation of Rubin et al. (2023) and the DES5Y sample (S'anchez et al. 2024; Vincenzi et al. 2024; DES Collaboration et al. 2024). DESI24 report evidence for a time varying equation-of-state with w 0 > -1 and w a < 0, but with a statistical significance that is strongly dependent on which SN sample was chosen to be combined with Planck CMB and DESI BAO measurements. Specifically, DESI24 find ∼ 2 . 5 σ , 3 . 5 σ and 3 . 9 σ evidence for dynamical dark energy using the Pantheon+, Union3 and DES5Y SN samples respectively. These numbers are reduced slightly to ∼ 2 . 2 σ , 3 . 1 σ and 3 . 5 σ respectively using a combined DESI+SDSS BAO compilation as described in Section 3.3 of DESI24. The Pantheon+ sample (as we will show below) is consistent with the Planck ΛCDM cosmology and so the DESI24 results for this SN compilation could plausibly be interpreted as a statistical fluctuation. However, the high statistical significance levels for the Union3 and DES5Y SN samples are unlikely to be statistical fluctuations and therefore deserve scrutiny.  \nIn this paper, I investigate the statistical consistency of the Pantheon+ and DES5Y SN samples. These two catalogues show the largest differences in the DESI24 analysis. The Union3 compilation for individual SN is not yet in the public domain and would, in any case, require a very different type of analysis to that presented here. The Pantheon+/DES5Y comparison is particularly simple because the DES5Y compilation has only a small number of SN at low redshifts with a high degree of overlap with low redshift SN in the Pantheon+ sample.  \nSection 2 describes the Pantheon+ and DES5Y SN samples and summarizes cosmological constraints on the parameters of the ΛCDM cosmology and the w 0 , w a parameterisation of Equ. 1 (which we denote as w 0 w a CDM). We cross-correlate Pantheon+ with DES5Y in Sect. 3, finding evidence for a systematic calibration difference between low and high redshifts. We repeat the parameter analysis of Sect. 2 after correcting the DES5Y sample for the calibration difference. Section 4 discusses the role of bias corrections in accounting for the calibration differences. Our conclusions are summarized in Sect. 5. We note that in a recent paper Dhawan et al. (2024) discuss various potential sources of redshift dependent systematic errors in SN photometry.", '2 THE PANTHEON+ AND DES5Y SN SAMPLES': "The construction of the Pantheon+ catalogue is complex as summarized in the flow diagram in Fig. 1 of Brout et al.  \nFigure 1. Residuals of the magnitude redshift relation relative to that expected in the best fit Planck TTTEEE ΛCDM cosmology. The grey bands show the Planck ± 1 σ and ± 2 σ error ranges. The red points show the maximum likelihood residuals for the SN data averaged in logarithmically space bins in (Hubble distance) redshift. The errors are computed from the full covariance matrices for the two SN catalogues. The upper panel shows the fits for the Pantheon+ catalogue and the lower panel for the DES5Y catalogue. The solid blue lines show the best fit ΛCDM cosmology and the dashed lines show the best fit w 0 w a CDM cosmology. The best fit parameters are listed in the Figure. Our fits retained 1417 and 1754 SN in the Pantheon+ and DES5Y samples respectively.  \n<!-- image -->  \n(2022a). The catalogue 'standardizes' observations from 20 supernova compilations spanning a wide redshift range from the local SN used in the SH0ES distance scale project (Riess et al. 2022) to a maximum redshift of 2 . 261. The crosscalibration of the photometric systems and corrections for biases, which involve forward modelling of the SN populations, are described in Brout & Scolnic (2021); Popovic et al. (2021); Brout et al. (2022b); Popovic et al. (2023). The Pantheon+ catalogue contains 203 spectroscopically confirmed Type Ia SN from the DES year 3 sample (Brout et al. 2019; Smith et al. 2020).  \nThe DES5Y SN sample consists of 1635 DES SN spanning the redshift range 0 . 0596 -1 . 12 together with 194 SN at redshifts z < 0 . 1 from a small number of more recent (post 2009) SN surveys. Historical low redshift SN samples are not included to simplify the cross-calibration analysis. As with Pantheon+, the construction of the DES5Y sample is complicated and is most succinctly summarized in Vincenzi et al. (2024). Several aspects of the DES5Y analysis are similar to those in Pantheon+. However, since most of the DES supernovae lack spectroscopic classification, the DES team apply the Bayesian classifier SuperNNova (see Kessler & Scolnic 2017; Moller & de Boissi'ere 2020, and references therein) to compute a probability that a SN belongs to the Type Ia population. The uncertainty in photometric classification is propagated into the covariance matrix. The catalogue lists the distance moduli, µ DES , of the SN assuming a Hubble constant of 70 km s -1 Mpc -1 . To convert to the magnitude  \nFigure 1 shows the residuals of the magnitude-redshift relations relative to the best fit Planck TTTEEE ΛCDM fit 1 . Here we compute the maximum likelihood value of the SN apparent magnitude in logarithmically spaced bins in redshift together with the diagonal errors computed from the full covariance matrices of the respective SN samples. Note that the binning is for plotting purposes only. All of the fits discussed in this paper have been done on the unbinned data. We use SN with 'Hubble distance' redshifts, z HD (i.e. corrected to the CMB frame and for peculiar velocities) and for both samples we use SN in the redshift range 0 . 02 ≤ z HD ≤ 1 . 2. In addition, we remove SN from DES5Y with magnitude errors δm > 1, since these have a low probability of being Type Ia SN based on the DES photometric data. This leaves 1417 entries in the Pantheon+ sample (out of a total of 1701 entries; note that in a few cases, Pantheon+ lists separately two or more observation of the same SN) and 1754 SN in DES5Y (out of a total of 1829). For reference, the χ 2 values for the Planck ΛCDM cosmology (Ω m = 0 . 3135 ± 0 . 0081) are 1259 . 6 for Pantheon+ and 1644 . 68 for DES5Y.  \n<!-- image -->  \n<!-- image -->  \nFigure 2. 68% and 95% contours for the marginalized posterior parameters in the w 0 -w a , w 0 -Ω m and w a -Ω m planes for the Pantheon+ (red) and DES5Y (blue) SN compilations. The dashed lines show the values for the best fit Planck ΛCDM cosmology.  \n<!-- image -->  \nsystem of Pantheon+ I apply the correction:  \nm DES = µ DES -19 . 33 , (2)  \nbased on my fits of the Planck best fit ΛCDM to the Pantheon+ sample to determine the SN peak absolute magnitude.  \n(i) Pantheon+: The ΛCDM best fit gives Ω m = 0 . 333 ± 0 . 018, slightly higher than the value of Ω m for best fit Planck ΛCDM cosmology and in agreement with the results of Brout et al. (2022a). The χ 2 value for this fit improves by only ∆ χ 2 = 1 . 2, thus the Pantheon+ sample is consistent with the Planck ΛCDM cosmology. There is no improvement in χ 2 compared to ΛCDM if w 0 and w a are allowed to vary. The Pantheon+ SN data therefore offer no support for models with a time varying equation-of-state.  \n(ii) DES5Y: The ΛCDM best fit gives Ω m = 0 . 354 ± 0 . 017 which is ∼ 2 . 2 σ higher than best fit Planck ΛCDM with an improvement in χ 2 of ∆ χ 2 = 5 . 1. However, allowing w 0 and w a to vary leads to a substantial reduction in χ 2 , and visually to a much better fit to the magnitude residuals. By adding w 0 and w a , the best fit is able to track the inflection between the low redshift SN and the DES SN (with smaller  \nerror bars) at z > 0 . 2. The DES5Y compilation clearly prefers evolving dark energy, with ∆ χ 2 = 12 . 5 for the best fit Planck ΛCDM cosmology and ∆ χ 2 = 7 . 4 for the best fit DES5Y ΛCDM cosmology. Thus, the Planck ΛCDMcosmology is strongly disfavoured by the DES5Y data (at roughly 3 σ ), and evolving dark energy is preferred over ΛCDM with high Ω m at ∼ 2 σ . This agrees with the results of Camilleri et al. (2024) who reconstruct the expansion rate from the DES5Y SN data and find that it differs from the expansion history expected in the Planck ΛCDM cosmology.  \nThe tension between the Pantheon+ and DES5Y datasets is clear from the parameter constraints plotted in Fig. 2. To produce Fig. 2 I applied uniform priors on the parameters Ω m , w 0 and w a as follows: For Pantheon+, 0 . 2 ≤ Ω m ≤ 0 . 6, -1 . 4 ≤ w 0 ≤ 0 . 4, -4 ≤ w a ≤ -0 . 4; For DES5Y, 0 . 01 ≤ Ω m ≤ 0 . 81, -2 ≤ w 0 ≤ 1, -10 ≤ w a ≤ 1. I applied a Planck ΛCDM Gaussian prior on H 0 with 67 . 44 ± 0 . 58 km s -1 Mpc -1 and treated the SN absolute magnitude M as a derived parameter. Since we are not combining the SN data with other cosmological data, the prior on H 0 has no impact on the results plotted in Fig. 2. Chains were computed with the MULTINEST nested sampler (Feroz et al. 2009, 2011). The best fit Planck ΛCDM parameters are shown by the dotted lines which intersect within the 1 σ contours for the Pantheon+ sample. In contrast, the DES5Y sample wants high values of Ω m , w 0 > -1 and and low values of w a < ∼ -2, favouring dynamical dark energy 2 . This, of course, is simply a consequence of the redshift dependence of the DES5Y magnitude-redshift relation shown in Fig. 1. The favouring of high values of Ω m is especially worrying since many different cosmological probes, including the CMB, BAO, galaxy power spectrum full shape analysis (e.g. Philcox & Ivanov 2022; D'Amico et al. 2024), cluster baryon fractions (Mantz et al. 2022) give concordant values of Ω m ≈ 0 . 3 to within a few percent, in strong disagreement with the values Ω m > ∼ 0 . 4 favoured by DES5Y.", 'Evolving dark energy': 'Table 1. The first column lists the name of the SN sample following the nomenclature in Scolnic et al. (2022). The second column lists the number of SN common to both the Pantheon+ and DES5Y catalogues. The third column gives the median redshift of the SN sample. Columns 4-7 list the mean magnitude difference of SN in common to Pantheon+ and DES5Y (column 4), the mean bias corrections applied to Pantheon+ (column 5) and DES5Y (column 6), the mean difference in the bias corrections applied to each catalogue (column 7) and the 1 σ error on each of these quantities. The CFA4P3 sample has only 3 SN and so we list only the means since the sample is too small to provide a meaningful error estimate. The final line lists the parameters for the combined sample of low redshift SN.  \nw = -1, see also Cortˆes & Liddle (2024)). In interpreting the DESI24 evidence for dynamical dark energy, it is important to consider the redshift range spanned by each dataset.  \nThe most direct tests of evolving dark energy come from direct geometric measures of the expansion history using standard rulers and standard candles. BAO measurements apply a standard ruler to measure the comoving angular diameter distance D M ( z ) and Hubble parameter H ( z ) as a function of redshift. As summarized in DESI24, BAO measurements covering the redshift range ∼ 0 . 3 -2 . 3, including the new measurements from DESI, are consistent with a ΛCDM expansion history. On their own, BAO measurements do not provide any evidence for evolving dark energy. DESI BAO measurements combined with Pantheon+ SN are consistent with ΛCDM. It is only when BAO are combined with Union3 or DES5Y SN data that a substantial preference for dynamical dark energy emerges (see Fig. 6 of DESI24). The dynamical dark energy models preferred by these data combinations are therefore extremely sensitive to the fidelity of the SN samples at low redshift.  \nIn this paper, we have cross-correlated the Pantheon+ and DES5Y supernova samples and found evidence for a calibration difference of ∼ 0 . 04 mag between low and high redshifts. Crudely correcting the DES5Y SN sample for this calibration difference brings the magnitude-redshift relation into near perfect agreement with the Planck ΛCDM cosmology, eliminating any need to invoke dynamical dark energy. The preference for evolving dark energy seen in the DES5Y sample may therefore be caused by a small systematic calibration error associated with the bias corrections applied to the low redshift SN in this catalogue (see Fig. 7). This is a plausible explanation since the cosmological parameters determined from DES5Y (see Fig. 2) are in tension with most other cosmological data, including BAO. Testing dynamical dark energy is very difficult, especially if the departures from ΛCDM set in at redshifts z < ∼ 0 . 2. At such low redshifts, SN offer the only geometrical probes of the expansion history. Inferences on dark energy are therefore sensitive to small calibration difference in standardizing SN data from different sources over a wide range in redshift (see also Dhawan et al. (2024)). The methodologies that have been developed to achieve standardization are complicated and heavily dependent on simulations. It is therefore very difficult for a  \nnon-expert to assess the fidelity of these catalogues. Yet it is very dangerous to treat SN compilations as black boxes in combination with other data. Given the interest in evolving dark energy generated by DESI24, there is an urgent need for a detailed intercomparison of the Pantheon+, Union3 and DES5Y catalogues. Stringent control of systematic errors is required if the SN data are to be used to claim evidence for new physics.', '3 COMPARISON OF PANTHEON+ AND DES5Y SN': "The DES5Y compilation uses only a small number of SN samples to probe the low redshift end ( z < ∼ 0 . 1) of the  \nFigure 4. The mean magnitude offset for SN common to Pantheon+ and DES5Y grouped by source catalogue. The numbers in brackets give the the number of SN common to both surveys. There are 3 SN in common in the CfA4P3 sample with a mean magnitude difference of of 0 . 028 ± 0 . 087 mag. which is not plotted because the error is so large (and unreliable).Figure 5. Magnitude redshift residuals as in Fig. 1 but correcting the subsamples in the DES5Y catalogue to remove the offsets of Fig. 4. The best fit ΛCDM cosmology is now very close to the best fit inferred from Planck .  \n<!-- image -->  \nmagnitude-redshift relation. The largest of these is the PanSTARRS Foundation Supernova Survey (Foley et al. 2018). 150 SN from the Foundation Survey are included in the Pantheon+ catalogue and 118 of these are also included in the DES5Y catalogue. The magnitude differences are plotted in the lower panel of Fig. 3. This shows a systematic offset between the Pantheon+ and DES5Y magnitudes of ⟨ m Pan -m DES ⟩ = -0 . 051 ± 0 . 007 mag (giving each SN equal weight). In addition, the DES5Y catalogue includes 68 SN from the Center for Astrophysics (CfA) SN surveys (Hicken et al. 2009, 2012) and 8 SN from the Carnegie Supernova Project (CSP, Krisciunas et al. 2017), 7 of which are included in Pantheon+. Figure 4 plots the Pantheon+/DES5Y offsets for these surveys. Most of the low redshift surveys are offset by ∼ 0 . 04 -0 . 05 mag. relative to the more distant DES supernovae. Such an offset can easily explain the differences between the Pantheon+ and DES5Y magnitude-redshift relations seen in Fig. 1. Table 1 lists the median redshift and mean magnitude offset for each sample.  \nTo illustrate this point, we have 'corrected' the DES5Y catalogue by adding the offsets from Fig. 4 to the DES5Y magnitudes. In effect, we are recalibrating the DES5Y catalogue to match Pantheon+. The residuals in the magnituderedshift relation are plotted in Fig. 5. which can be compared directly to the DES5Y plot shown on Fig. 1. The best  \n<!-- image -->  \n<!-- image -->  \nFigure 6. Parameter constraints as in Fig. 2 but now using DES5Y magnitudes corrected to remove the offsets of Fig. 4.  \n<!-- image -->  \nFigure 7. The mean magnitude offset for SN common to Pantheon+ and DES5Y grouped by source catalogue (as in Fig. 4) plotted against the mean bias correction ( ⟨ bias DES ⟩ ) computed in the DES5Y catalogue. The numbers in brackets give the the number of SN common to both surveys.  \n<!-- image -->  \nfit ΛCDM cosmology now has a value of Ω m in near perfect agreement with the Planck ΛCDM cosmology. Allowing w 0 and w a to vary leads to a reduction in χ 2 of only 3 (driven mainly by the low point at z ∼ 1). Evidently, the recalibrated DES5Y catalogue does not show a statistically significant preference for a time varying equation-of-state.  \nThe parameter plots of Fig. 2 illustrate the tension between the Pantheon+ and DES5Y SN samples. Using the recalibrated DES5Y catalogue we find the parameter constraints shown in Fig. 6. As expected, there is now much greater overlap between Pantheon+ and DES5Y and both surveys are consistent with the ΛCDM expectation of w 0 = -1, w a = 0. The corrected DESY5 constraints are still skewed to high values of Ω m as a consequence of the negative residual at z > 1 in Fig. 5.", '4 EFFECTS OF BIAS CORRECTIONS': "As discussed above, both Pantheon+ and the DES5Y apply simulation based corrections to correct for selection biases. These bias corrections are computed from simulations that require knowledge of the true distribution of light curves  \nparameters, colour distributions, intrinsic scatter and dependence on host-galaxy properties (e.g. a colour dependent 'mass-step' correction). Since these properties must be determined from incomplete data and are poorly understood, the bias corrections are a potential source of systematic photometric error.  \nTable 1 lists the mean bias corrections applied to each sample in both the Pantheon+ and DES5Y catalogues. The bias corrections applied to Pantheon+ are generally small. For the DES spectroscopic sample (listed as DES5Y), the mean bias correction is -0 . 0089 in Pantheon+ and -0 . 0158 in the DES5Y catalogue, and the mean difference in bias corrections is -0 . 0069 accounting for about half the measured offset of ⟨ m Pan -m DES ⟩ = -0 . 012. However, for the low redshift SN, the mean bias corrections in the DES5Y catalogue are large and correlate strongly with the mean magnitude offsets presented in the previous section. This is illustrated in Fig. 7 which plots the mean magnitude offset against the mean bias computed in the DES5Y catalogue. Evidently, bias corrections in the DES5Y catalogue are resposible for the ∼ 0 . 04 offset between high and low redshift SN identified in the previous section. The last line in Table 1 averages over all of the low redshift SN and reinforce the points made in this paragraph at high statistical significance. There is a high degree of overlap between the low redshift SN samples in the Pantheon+ and DES5Y catalogues and there is no good reason why the bias corrections in the two catalogues should differ. This raises the possibility that systematic errors in the bias corrections are responsible for the differences in the cosmological results from Pantheon+ and DES5Y.", '5 DISCUSSION AND CONCLUSIONS': "The elusive nature of dark energy has formed an important part of the science cases for several ambitious projects that are either underway or will soon be taking data (e.g DESI Collaboration et al. 2016; Amendola et al. 2018; Mao et al. 2022). The effectiveness of these projects has often been judged in terms of a 'figure of merit' defined as the inverse of the area contained within the 95% confidence contours in the w 0 -w a plane (Albrecht et al. 2006). However, the figure of merit gives an incomplete picture since the area in w 0 -w a space accessible to a single, or combination, of experiments depends on their redshift range (recognized by Albrecht et al. (2006) via the definition of a sample dependent pivot value of w p with which to test for deviations from", '6 ACKNOWLEDGEMENTS': 'I thank the Leverhulme Foundation for the award of a Leverhulme Emeritus Fellowship. I am grateful to Maria Vincenzi for answering my questions on the DES5Y analysis and to her and Suhail Dhawan for comments on the manuscript.', 'DATA AVAILABILITY': 'No new data were generated or analysed in support of this research.', 'REFERENCES': "Alam S., et al., 2017, MNRAS, 470, 2617  \n```\nAlam S., et al., 2021, Phys. Rev. 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