Cosmological Models with Variable Gravitational and Cosmological constants in $R^{2}$ Gravity

TL;DR

This paper explores how the universe's evolution is affected by variable gravitational and cosmological constants within $R^2$ gravity, providing new solutions relevant for cosmological modeling.

Contribution

It introduces new cosmological solutions in $R^2$ gravity with variable constants, extending previous models to include radiation and matter eras.

Findings

Derived cosmological solutions with variable constants

Analyzed universe evolution in higher derivative gravity

Provided models applicable to different cosmic eras

Abstract

We consider the evolution of a flat Friedmann-Roberstson-Walker Universe in a higher derivative theories, including $\alpha R^{2}$ terms to the Einstein-Hilbert action in the presence of a variable gravitational and cosmological constants. We study here the evolution of the gravitational and cosmological constants in the presence of radiation and matter domination era of the universe. We present here new cosmological solutions which are physically interesting for model building.