http://arxiv.org/abs/2305.02863
The fluctuation of matter parameter $\sigma_8$ is by model construction degenerate with the growth index $\gamma$. Here we try to study the effect on the cosmological parameters constraints from treating each independently by considering $\sigma_8$ as a free and not derived parameter along with $\gamma$, to then try to constrain all by three probes, namely the CMB spectrum, the growth measurements from redshift space distortions $f\sigma_8$ and the galaxy cluster counts. We also want to asses the impact of this relaxation on the $\sigma_8$ tension. We also propose a more sophisticated correction, along with the classical one that takes into account the impact of cosmology on the growth measurements, which is to adjust the growth to keep the observed power spectrum invariant with the background evolution. We found that untying the two parameters does not shift the maximum likelihood on either $\sigma_8$ or $\gamma$ but rather allow for larger bounds with respect to when $\sigma_8$ is a derived parameter. More precisely, we obtain $\sigma_8 = 0.809\pm 0.043 $ and $\gamma = 0.613\pm 0.046$ in agreement with Planck constraints for the former and compatible with $\Lambda$CDM for the latter but with bounds enough wide to accomodate both values subject of tensions for $\sigma_8$. On the other hand, considering a tier correction yields $\sigma_8 = 0.734\pm 0.013$ close to the local values albeit with a growth index $\gamma = 0.636\pm 0.022$ while allowing a massive neutrinos yielded $\sigma_8 = 0.756\pm 0.024$, still preferring low values but with looser constraints, with $\gamma = 0.549\pm 0.048$ and a slight preference for $\Sigma m_\nu \sim 0.19$ value. We conclude that untying $\sigma_8$ and $\gamma$ helps in relieving the discomfort on the former between CMB and local probes and that careful analyse should be followed when using data obtained in a model dependent way.(abridged)
Z. Sakr
Fri, 5 May 23
6/67
Comments: Prepared for a contribution to the special issue on Modified Gravity Approaches to the Tensions of {\Lambda}CDM