Remembrance of Things Past

TL;DR

This paper extends the analysis of nonlinear sigma models on de Sitter space to general cosmological backgrounds, providing analytic and numerical results that show how primordial inflation influences late-time universe behavior.

Contribution

It generalizes the resummation of large logarithms from de Sitter to arbitrary cosmological backgrounds using an analytic approximation.

Findings

Large-scale effects of primordial inflation are transmitted to late times.

Analytic expressions for the scalar propagator approximation.

Numerical results demonstrate evolution in realistic expansion histories.

Abstract

Nonlinear sigma models on de Sitter background have proved a useful prototype for quantum gravity in summing the large logarithms which arise from loop corrections. We consider a model whose evolution is described, at leading logarithm order, by the trace of the coincident, doubly differentiated scalar propagator. An analytic approximation for this quantity on an arbitrary expansion history is applied to generalize the resummed de Sitter result to any cosmological background which has experienced primordial inflation. In addition to analytic expressions, we present explicit numerical results for the evolution in a plausible expansion history. The large scales of primordial inflation are transmitted to late times.