Testing Dark energy models in the light of $\sigma_8$ tension

TL;DR

This paper investigates how measurements of  and m can test dark energy models, finding that some models worsen the  tension while others alleviate it, highlighting the importance of  data in testing modified gravity.

Contribution

It compares the effects of two dark energy models on  tension, showing their different impacts and providing bounds on neutrino mass within these models.

Findings

HS model worsens  tension

DDE model alleviates  tension

Neutrino mass bounds vary with models

Abstract

It has been pointed out that there exists a tension in $\sigma_8-\Omega_m$ measurement between CMB and LSS observation. In this paper we show that $\sigma_8-\Omega_m$ observations can be used to test the dark energy theories. We study two models, (1) Hu-Sawicki(HS) Model of $f(R)$ gravity and (2) Chavallier-Polarski-Linder(CPL) parametrization of dynamical dark energy (DDE), both of which satisfy the constraints from supernovae. We compute $\sigma_8$ consistent with the parameters of these models. We find that the well known tension in $\sigma_8$ between Planck CMB and large scale structure (LSS) observations is (1) exacerbated in the HS model and (2) somewhat alleviated in the DDE model. We illustrate the importance of the $\sigma_8$ measurements for testing modified gravity models. Modified gravity models change the matter power spectrum at cluster scale which also depends upon the neutrino mass. We present the bound on neutrino mass in the HS and DDE model.