Cosmological density perturbations with a scale-dependent Newton’s constantG

Abstract

We explore possible cosmological consequences of a running Newton's constant $G(\ensuremath{\square})$, as suggested by the nontrivial ultraviolet fixed point scenario in the quantum field-theoretic treatment of Einstein gravity with a cosmological constant term. In particular, we focus here on what possible effects the scale-dependent coupling might have on large scale cosmological density perturbations. Starting from a set of manifestly covariant effective field equations derived earlier, we systematically develop the linear theory of density perturbations for a nonrelativistic, pressureless fluid. The result is a modified equation for the matter density contrast, which can be solved and thus provides an estimate for the growth index parameter $\ensuremath{\gamma}$ in the presence of a running $G$. We complete our analysis by comparing the fully relativistic treatment with the corresponding results for the nonrelativistic (Newtonian) case, the latter also with a weakly scale-dependent $G$.