Linear Nash perturbations with a CMB+Pantheon+H(z) and BAO+DES Y1 joint analysis of cosmic growth expansion

Abstract

We test a model associated with the Einstein gravity modified by using the linear Nash perturbations of the background metric. By means of a Markov chain Monte Carlo (MCMC) modeling, we combine the recent Dark Energy Survey (DES Y1) with the baryon acoustic oscillations (BAO) measurements and a larger datasets of ``Gold 2018'' growth data, the Planck $2018/\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ parameters on the cosmic microwave background (CMB), the Pantheon Supernovae type Ia and the Hubble parameter data with redshift ranging from $0.01<z<2.3$ to derive the related constraints on the model parameters. We use the Jeffreys' scale to perform the Akaike information criterion (AIC) to ascertain the statistical viability of the model in comparison with the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. We find a mild reduction of the ${\ensuremath{\sigma}}_{8}$ discrepancy between the best-fit values of growth-rate amplitude factor and the matter content $({\ensuremath{\sigma}}_{8}\ensuremath{-}{\mathrm{\ensuremath{\Omega}}}_{m})$ of the observations from CMB and large scale structure (LSS) probes. Due to the degeneracy of the model parameters, this situation may be improved. Oppositely, in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ context, the situation is aggravated. For the considered large dataset, the discrepancy of best-fit values persists in both $({\ensuremath{\sigma}}_{8}\ensuremath{-}{\mathrm{\ensuremath{\Omega}}}_{m})$ and $(h\ensuremath{-}{\mathrm{\ensuremath{\Omega}}}_{m})$ planes and reinforces the mismatch of the Hubble parameter in CMB and BAO probes.