Testing the effect of $H_0$ on $f\sigma_8$ tension using a Gaussian Process method

TL;DR

This study employs a Gaussian Process approach to analyze how different priors of the Hubble constant $H_0$ influence the $f\sigma_8$ tension, revealing that higher $H_0$ priors can alleviate discrepancies in cosmological parameters.

Contribution

It introduces a Gaussian Process-based method to reconstruct $H(z)$ from observational data, assessing the impact of $H_0$ priors on the $\sigma_8^0-\Omega_m^0$ tension and parameter degeneracies.

Findings

Higher $H_0$ priors reduce the $\sigma_8^0-\Omega_m^0$ tension.

Using $H_0$ from Planck alleviates tension to less than $1\sigma$.

Applying HST $H_0$ prior increases tension beyond $2\sigma$.

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.