Quantum Cosmology in Accelerating Spacetimes II

TL;DR

This work develops leading-logarithm gravitational equations for accelerating spacetimes to capture nonperturbative quantum gravity effects during inflation. By reducing the full equations to a tractable set involving $A_{ij}, B_i, C$ in the ADM framework, the authors demonstrate that the leading logs can be resummed and verified against perturbative results, yielding explicit 2-loop secular corrections. They show that the graviton mode function acquires a time-dependent correction $u(t,\mathbf{k}) = u_0(t,\mathbf{k})\left[1 + \tfrac{9}{8}\lambda^2 T^2 + \cdots\right]$ and that the tensor power spectrum is accordingly modified, while the Newtonian potential receives a $\ln[aHr]$-type secular correction $C(t,r) = \frac{GM}{a r}\left[1 - \frac{\kappa^2 H^2}{4\pi^2}\ln[aHr] + \cdots\right]$. The framework thus provides a consistent, potentially nonperturbative avenue to explore late-time cosmological implications of quantum gravity during inflation and to connect perturbative loops with a nonperturbative evolution.

Abstract

This paper is a sequel in which we further analyze the recently derived quantum gravity equations which apply in accelerating cosmological spacetimes and whose solutions should be equivalent to all order re-summations of the perturbative leading logarithms that appear. In particular we study their implications concerning the primordial tensor power spectrum and the gravitational force due to a test source.