Isotropic universe with almost scale-invariant fourth-order gravity

TL;DR

This paper investigates isotropic vacuum cosmologies in fourth-order gravity with scale-invariant Lagrangians, deriving exact solutions and analyzing their inflationary behavior, including modifications from de Sitter to power-law inflation.

Contribution

It provides closed-form solutions for flat Friedmann models in a broad class of scale-invariant fourth-order gravity theories, highlighting how additional terms alter inflationary dynamics.

Findings

Exact solutions for flat Friedmann cosmologies in specified gravity models.

Demonstration of transition from de Sitter to power-law inflation via G ln G term.

Identification of attractor solutions influencing early and late-time universe behavior.

Abstract

We study a broad class of isotropic vacuum cosmologies in fourth-order gravity under the condition that the gravitational Lagrangian be scale-invariant or almost scale-invariant. The gravitational Lagrangians considered will be of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) = G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat Friedmann space-time and interpret their asymptotic early-time and late-time behaviour as well as their inflationary stages. One unique example which we discuss is the case of a very small negative value of the parameter b in the Lagrangian L = R^2 + b G ln G which leads to the replacement of the exact de Sitter solution from L = R^2 (being a local attractor) to a power-law inflation exact solution also representing a local attractor. This shows how one can modify the dynamics from de Sitter to power-law inflation by the addition of the G ln G-term.