Growth of matter density perturbations in 4D Einstein-Gauss-Bonnet gravity

Recently, a novel Einstein-Gauss-Bonnet gravity in four dimensions has been introduced [Phys. Rev. Lett. 124 (2020) 081301]. We will investigate cosmological consequences of this model in details. We will consider linear matter density perturbations and also estimate relevant modified gravity parameters. Specially we will concentrate on the growth rate of non-relativistic matter perturbations on top of FRW geometry and show that for a narrow range of the Gauss-Bonnet coupling constant, observational data will be satisfied. In this paper, it is shown that for enough large values of the coupling constant, the suggested $\sigma_8$ will become greater than $\Lambda$CDM value.