On analytical solutions of f(R) modified gravity theories in FLRW cosmologies

TL;DR

This paper introduces a new analytical method for solving f(R) modified gravity theories in FLRW cosmologies, providing explicit solutions and demonstrating applications to inflation and late-time acceleration.

Contribution

A novel analytical approach for f(R) theories in FLRW spacetimes that simplifies equations and enables explicit solutions for specific actions.

Findings

Analytical solutions for power-law f(R) actions.

Method validated by numerical agreement.

Potential applications to inflation and late-time acceleration.

Abstract

A novel analytical method for f(R) modified theories without matter in Friedmann-Lemaitre-Robertson-Walker spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the Ricci scalar R with the Hubble parameter H. The solution of equation of motion for actions of the form of power law in Ricci scalar R, is presented with a detailed elaboration of the action quadratic in R. The reverse use of the introduced method is exemplified in finding functional forms f(R) which lead to specified scale factor functions. The analytical solutions are corroborated by numerical calculations with excellent agreement. Possible further applications to the phases of inflationary expansion and late-time acceleration as well as f(R) theories with radiation are outlined.