On the evolution of the Hubble constant with the SNe Ia Pantheon Sample and Baryon Acoustic Oscillations: a feasibility study for GRB-cosmology in 2030

Abstract

The difference from 4 to 6 $\sigma$ in the Hubble constant ($H_0$) between the values observed with the local (Cepheids and Supernovae Ia, SNe Ia) and the high-z probes (CMB obtained by the Planck data) still challenges the astrophysics and cosmology community. Previous analysis has shown that there is an evolution in the Hubble constant that scales as $f(z)={\mathcal{H}}_0/(1+z{)}^{\eta }$, where ${\mathcal{H}}_0$ is $H_0(z=0)$ and $\eta$ is the evolutionary parameter. Here, we investigate if this evolution still holds by using the SNe Ia gathered in the Pantheon sample and the BAOs. We assume $H_0=70{\text{km s}}^{-1}{\text{Mpc}}^{-1}$ as the local value and divide the Pantheon into 3 bins ordered in increasing values of redshift. Similar to our previous analysis but varying two cosmological parameters contemporaneously ($H_0$, ${\Omega }_{0m}$ in the $\Lambda$CDM model and $H_0$, $w_a$ in the $w_0{w}_a$CDM model), for each bin we implement a MCMC analysis obtaining the value of $H_0$ $[...]$. Subsequently, the values of $H_0$ are fitted with the model $f(z)$. Our results show that a decreasing trend with $\eta \sim 10^{-2}$ is still visible in this sample. The $\eta$ coefficient reaches zero in 2.0 $\sigma$ for the $\Lambda$CDM model up to 5.8 $\sigma$ for $w_0{w}_a$CDM model. This trend, if not due to statistical fluctuations, could be explained through a hidden astrophysical bias, such as the effect of stretch evolution, or it requires new theoretical models, a possible proposition is the modified gravity theories, $f(R)$ $[...]$. This work is also a preparatory to understand how the combined probes still show an evolution of the $H_0$ by redshift and what is the current status of simulations on GRB cosmology to obtain the uncertainties on the ${\Omega }_{0m}$ comparable with the ones achieved through SNe Ia.

45 pages, 6 figures, 3 tables, added references, final version after proofs corrections, published in Galaxies

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