theory of gravity can survive the above-mentioned observations. Actually, the investigation of the expected constraints on DGP braneworld cosmology has been performed from different astrophysical observations [@Xu10; @Giannantonio; @Lombriser; @Wang08]. However, it is interesting to note that based on different theoretical basis, the determination of the same cosmological parameter in different cosmological models are clearly different. The normal branch of DGP gravity is confronted by the currently available cosmic observations from the geometrical and dynamical perspectives. For instance, ref. @Xu14 made a joint analysis of the DGP braneworld cosmology with the Supernova Legacy Survey (SNLS) data, first released CMB data from Planck, and redshift space distortion (RSD) data ($\Omega_m=0.286\pm 0.008$). While comparing the results with those obtained from Planck 2018 data (TT, TE, EE+lowE+lensing) based $\Lambda$CDM model $\Omega_m=0.315\pm0.007$ [@Aghanim], differences in central values of the best-fit cosmological parameter were clearly reported. Similar analyses were carried out by @Ma19. If one wants to place more comprehensive cosmological constraints on a possible model or distinguish between dark energy and modified gravity theories, it is crucial to measure the expansion rate of universe at many different redshifts.

The power of modern cosmology lies in building up consistency rather than in single, precise, crucial 