Test the effects of $H_0$ on $f\\sigma_8$ tension with 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 a great influence 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 $H_0 = 73.52 \\pm 1.62$ resulted from the Hubble Space Telescope photometry.