The initial state of generalized radiation universes

TL;DR

This paper investigates the early-time stability and initial conditions of radiation-filled, isotropic, and homogeneous universes in quadratic gravity theories, revealing their asymptotic behavior and stability properties.

Contribution

It provides a comprehensive asymptotic analysis of the initial state of radiation universes in quadratic gravity, including stability results and a formal series representation near the singularity.

Findings

Proves stability and uniqueness of asymptotic solutions in most quadratic gravity models.

Derives a formal series solution near the initial singularity dominated by subdominant curvature and radiation.

Identifies potential exceptions in conformally invariant Bach-Weyl gravity.

Abstract

We use asymptotic methods to study the early time stability of isotropic and homogeneous solutions filled with radiation which are close initially to the exact, flat, radiation solution in quadratic lagrangian theories of gravity. For such models, we analyze all possible modes of approach to the initial singularity and prove the essential uniqueness and stability of the resulting asymptotic scheme in all cases except perhaps that of the conformally invariant Bach-Weyl gravity. We also provide a formal series representation valid near the initial singularity of the general solution of these models and show that this is dominated at early times by a form in which both curvature and radiation play a subdominant role. We also discuss the implications of these results for the generic initial state of the theory.