Testing the effect of $H_0$ on $fsigma_8$ tension using a Gaussian Process method. (arXiv:1911.12076v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Li_E/0/1/0/all/0/1">En-Kun Li</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Du_M/0/1/0/all/0/1">Minghui Du</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zhou_Z/0/1/0/all/0/1">Zhi-Huan Zhou</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zhang_H/0/1/0/all/0/1">Hongchao Zhang</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Xu_L/0/1/0/all/0/1">Lixin Xu</a>
Using the $fsigma_8(z)$ 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 $1sigma$) when taking a prior for
$H_0$ obtained from PLA. Moreover, the tension exceeds $2sigma$ 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.
Using the $fsigma_8(z)$ 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 $1sigma$) when taking a prior for
$H_0$ obtained from PLA. Moreover, the tension exceeds $2sigma$ 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.
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