Asymptotics of flat, radiation universes in quadratic gravity

TL;DR

This paper analyzes the early and late time behavior of flat, radiation-dominated universes in quadratic gravity, showing initial singularities and that the known general relativity solution dominates late-time asymptotics.

Contribution

It provides a detailed asymptotic analysis of flat radiation universes in quadratic gravity, highlighting the persistence of singularities and the dominance of general relativity solutions at late times.

Findings

All universes are initially singular.

Late time behavior aligns with general relativity solutions.

No solutions diverge faster than e^{t^2}.

Abstract

We consider the asymptotics of flat, radiation-dominated isotropic universes in four-dimensional theories with quadratic curvature corrections which may arise when contributions related to the string parameter $\alpha'$ are switched on. We show that all such universes are singular initially, and calculate all early time asymptotics using the method of asymptotic splittings. We also examine the late time asymptotic behaviour of these models and show that there are no solutions which diverge as $e^{t^2}$, the known radiation solution of general relativity is essentially the only late time asymptotic possibility in these models.