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

Understand

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.