Asymptotic vacua with higher derivatives

TL;DR

This paper analyzes the behavior of vacuum universes with higher derivatives, revealing their asymptotic states and stability properties, which has implications for early universe cosmology and singularity transitions.

Contribution

It provides a comprehensive analysis of the asymptotic behavior of higher-derivative vacuum universes, including flat, open, and closed models, and relates findings to ekpyrotic and cyclic cosmology.

Findings

Flat vacua are attracted to a standard scaling solution.

Open vacua approach Milne states in both temporal directions.

Closed universes exhibit complex logarithmic singularities.

Abstract

We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.