Asymptotic states of generalized universes with higher derivatives

TL;DR

This paper reviews research on the asymptotic behavior of isotropic universes in higher-derivative theories, focusing on vacuum and radiation-filled cases near singularities using asymptotic splitting methods.

Contribution

It introduces a formal Fuchsian-type series approach to analyze the asymptotic states of generalized universes with higher derivatives.

Findings

Solutions are valid near collapse or big rip regimes

Uses asymptotic splittings of vector fields

Provides formal series solutions for universe dynamics

Abstract

We review ongoing research related to the asymptotic dynamics of isotropic universes in theories with higher derivatives, especially near the initial singularity. We treat two major cases, that is universes in vacuum, and also those filled with radiation using the method of asymptotic splittings of vector fields. Our solutions have the form of formal Fuchsian-type series for the basic unknowns and are valid near collapse or big rip regimes asymptotically.