Cosmological Exact Solutions in Some Modified Gravitational Theories

TL;DR

This paper derives exact cosmological solutions in modified gravity theories, specifically in power-law $f(R)$ gravity and Brans-Dicke models, providing insights into their behavior in different conformal frames.

Contribution

It introduces new exact solutions for power-law $f(R)$ gravity and Brans-Dicke theory in both Einstein and Jordan frames, extending the understanding of scalar-tensor cosmologies.

Findings

Exact solutions for power-law $f(R)$ gravity.

Exact solutions for Brans-Dicke theory with exponential potentials.

Solutions applicable to scalar-tensor theories with exponential scalar coupling.

Abstract

In a homogenous and isotropic cosmology, we introduce general exact solutions for some modified gravity models. In particular, we introduce exact solutions for power-law $f(R)$ gravity and Brans-Dicke theory in Einstein and Jordan conformal frames. In the Brans-Dicke case, the solutions are presented for both single and double exponential potentials in Einstein frame which correspond to power-law potentials in Jordan frame. Our analysis for extracting general exact solutions can also be generalized to those scalar-tensor theories in which the scalar field has an exponential coupling to Ricci scalar.