Quantum Gravity and Cosmological Density Perturbations

Abstract

We explore the possible cosmological consequences of a running Newton's constant, G(2), as suggested by the non-trivial ultraviolet fixed point scenario for Einstein gravity with a cosmological constant term. Here, we examine what possible effects a scale-dependent coupling might have on large-scale cosmological density perturbations. Starting from a set of manifestly covariant effective field equations, we develop the linear theory of density perturbations for a non-relativistic perfect fluid. The result is a modified equation for the matter density contrast, which can be solved and thus provides an estimate for the corrections to the growth index parameter, γ.

Ultraviolet Divergences and Scale-Dependent Gravitational Couplings

“…not scale dependent) Newton's constant one has the well know result f = 0.6028 and exponent γ = 0.5562. An explicit calculation in the presence of a running G and for a matter fraction Ω ≈ 0.25 gives, to lowest linear order in the small quantum correction c 0 [25], γ = 0.5562 − c q c a .…”

“…In the presence of a G(✷) the above equations need to be re-derived and amended [25], starting from the covariant field equations of Eq. (56) in the cN gauge of Eq.…”