  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.
