Testing the effect of $H_0$ on $f{\sigma }_8$ tension using a Gaussian Process method

Abstract

Using the $f{\sigma }_8(z)$ redshift space distortion (RSD) data, the ${\sigma }_8^0-{\Omega }_m^0$ tension is studied utilizing a parameterization of growth rate $f(z)={\Omega }_m(z{)}^{\gamma }$. Here, $f(z)$ is derived from the expansion history $H(z)$ which is reconstructed from the observational Hubble data applying the Gaussian Process method. It is found that different priors of $H_0$ have great influences on the evolution curve of $H(z)$ and the constraint of ${\sigma }_8^0-{\Omega }_m^0$. When using a larger $H_0$ prior, the low redshifts $H(z)$ deviate significantly from that of the $\Lambda$CDM model, which indicates that a dark energy model different from the cosmological constant can help to relax the $H_0$ tension problem. The tension between our best-fit values of ${\sigma }_8^0-{\Omega }_m^0$ and that of the \textit{Planck} 2018 $\Lambda$CDM (PLA) will disappear (less than $1\sigma$) when taking a prior for $H_0$ obtained from PLA. Moreover, the tension exceeds $2\sigma$ level when applying the prior $H_0=73.52\pm 1.62$ km/s/Mpc resulted from the Hubble Space Telescope photometry. By comparing the $S_8-{\Omega }_m^0$ planes of our method with the results from KV450+DES-Y1, we find that using our method and applying the RSD data may be helpful to break the parameter degeneracies.

13 pages, 10 figures, accepted for publication by MNRAS