On Ellis' programme within fourth order gravity

TL;DR

This paper investigates the asymptotic behavior of certain fourth order gravity models, demonstrating convergence to Einstein-de Sitter cosmology, using scalar field equivalence and averaging techniques.

Contribution

It establishes the late-time dynamics of non-tachyonic curvature squared gravity models and applies scalar field methods to analyze anisotropic cosmologies.

Findings

Bianchi I models tend to Einstein-de Sitter universe at late times

Averaging over oscillations reveals dust-like behavior

Scalar field equivalence simplifies the analysis of complex gravity models

Abstract

For the non-tachyonic curvature squared action we show that the expanding Bianchi-type I models tend to the dust-filled Einstein-de Sitter model for t tending to infinity if the metric is averaged over the typical oscillation period. Applying a conformal equivalence between curvature squared action and a minimally coupled scalar field (which holds for all dimensions > 2) the problem is solved by discussing a massive scalar field in an anisotropic cosmological model.