Testing dark energy models in the light of $$\sigma _8$$ σ8 tension

Abstract It has been pointed out that there exists a tension in $$\sigma _8-\varOmega _m$$ σ8-Ωm measurement between CMB and LSS observation. In this paper we show that $$\sigma _8-\varOmega _m$$ σ8-Ωm 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 $$\sigma _8$$ σ8 consistent with the parameters of these models. We find that the well known tension in $$\sigma _8$$ σ8 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 $$\sigma _8$$ σ8 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