# Cosmological Asymptotics in Higher-Order Gravity Theories

## TL;DR

This paper analyzes the early-time behavior of higher-order gravity cosmological models, revealing universal asymptotic solutions and stability properties that inform initial conditions and potential cyclic universe scenarios.

## Contribution

It provides a comprehensive asymptotic analysis of higher-derivative gravity cosmologies, identifying universal attractors and stability features near the initial singularity.

## Key findings

- Flat vacua are attracted to a universal square root scaling solution.
- Open vacua approach Milne states asymptotically.
- Radiation-filled universes are dominated by the t^{1/2} solution, with exceptions.

## Abstract

We study the early-time behavior of isotropic and homogeneous solutions in vacuum as well as radiation-filled cosmological models in the full, effective, four dimensional gravity theory with higher derivatives. We use asymptotic methods to analyze all possible ways of approach to the initial singularity of such universes. In order to do so, we construct autonomous dynamical systems that describe the evolution of these models, and decompose the associated vector fields. We prove that, at early times, all flat vacua as well as general curved ones are globally attracted by the "universal" square root scaling solution. Open vacua, on the other hand show in both, future and past directions a dominant asymptotic approach to horizon-free, Milne states that emerge from initial data sets of smaller dimension. Closed universes exhibit more complex logarithmic singularities. Our results on asymptotic stability show a possible relation to cyclic and ekpyrotic cosmologies at the passage through the singularity. In the case of radiation-filled universes of the same class we show the essential uniqueness and stability of the resulting asymptotic scheme, once more dominated by $t^{1/2}$, in all cases except perhaps that of the conformally invariant Bach-Weyl gravity. In all cases, we construct a formal series representation valid near the initial singularity of the general solution of these models and prove that curvature as well as radiation play a subdominant role in the dominating form. A discussion is also made on the implications of these results for the generic initial state of the theory.