Early universe cosmological solutions in exponential gravity

TL;DR

This paper explores exponential $f(R)$ gravity models in the early universe, demonstrating their ability to produce nonsingular bouncing solutions, de-Sitter states, and potentially new cosmological solutions, while remaining free of certain instabilities.

Contribution

It introduces exponential $f(R)$ gravity as a viable model for early universe cosmology with stable bouncing and de-Sitter solutions, highlighting its stability and novel solution possibilities.

Findings

Supports nonsingular bouncing solutions in matter and vacuum backgrounds.

Admits stable de-Sitter solutions due to positive derivatives of $f(R)$.

Suggests potential for new cosmological solutions unique to higher derivative theories.

Abstract

In this work we present some cosmologically relevant solutions using the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in metric $f(R)$ gravity where the form of the gravitational Lagrangian is given by $\frac{1}{\alpha}e^{\alpha R}$. In the low curvature limit this theory reduces to ordinary Einstein-Hilbert Lagrangian together with a cosmological constant term. Precisely because of this cosmological constant term this theory of gravity is able to support nonsingular bouncing solutions in both matter and vacuum background. Since for this theory of gravity $f^{\prime}$ and $f^{\prime\prime}$ is always positive, this is free of both ghost instability and tachyonic instability. Moreover, because of the existence of the cosmological constant term, this gravity theory also admits a de-Sitter solution. Lastly we hint towards the possibility of a new type of cosmological solution that is possible only in higher derivative theories of gravity like this one.