Cosmological Density Perturbations with a Scale-Dependent Newton's G

TL;DR

This paper investigates how a scale-dependent Newton's G, suggested by quantum gravity theories, affects large-scale cosmological density perturbations and the growth of structure in the universe.

Contribution

It develops a linear perturbation theory incorporating a running G and compares relativistic and Newtonian results, providing new insights into quantum gravity effects on cosmology.

Findings

Modified growth index parameter $$ due to running G.

Relativistic and Newtonian results show consistent effects.

Quantitative estimates of density perturbation growth with scale-dependent G.

Abstract

We explore possible cosmological consequences of a running Newton's constant $ G ( \Box ) $, as suggested by the non-trivial 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 non-relativistic, pressure-less 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 $\gamma$ in the presence of a running $G$. We complete our analysis by comparing the fully relativistic treatment with the corresponding results for the non-relativistic (Newtonian) case, the latter also with a weakly scale dependent $G$.