Quantum Cosmology in Accelerating Spacetimes

TL;DR

The paper develops leading-log all-orders (LLOG) equations for gravity in accelerating spacetimes to resum perturbative logarithms arising during inflation. By framing gravity as a quantum effective field theory with dimensional regularization and an ADM-based decomposition, it derives a simplified LLOG system whose solutions couple a dynamical background mode $A_{ij}$ to constrained fields. It then tests the null hypothesis of no quantum gravitational backreaction, showing that the LLOG dynamics generate time-growing corrections and a nonzero backreaction consistent with slow-down of expansion, and constructs a gauge-invariant expansion-rate observable to quantify this effect. The results suggest that gravitational backreaction can slow or terminate inflation and motivate pursuing non-perturbative extraction of the full LLOG behavior, offering a tractable path beyond perturbation theory. The framework also clarifies the range of validity and breakdown scale for LLOG equations, setting the stage for future work on non-perturbative evolution during the inflationary era.

Abstract

We simplify the gravitational equations which apply in accelerating spacetimes and are consistent with the cosmological principle. Solutions to these equations should be tantamount to all order re-summations of the perturbative leading logarithms. We discuss the null hypothesis and we study the local expansion rate observable.