Cosmological Solutions in Scalar-Tensor theory via the Eisenhart-Duval lift

TL;DR

This paper uses the Eisenhart-Duval lift to transform scalar-tensor cosmological models into linear equations, enabling the construction of analytic solutions in modified gravity theories like $f(R)$ and hybrid metric-Palatini gravity.

Contribution

It introduces a geometric method to linearize scalar-tensor cosmological equations, facilitating the derivation of analytic solutions in modified gravity models.

Findings

Successfully linearized scalar-tensor equations using Eisenhart-Duval lift.

Constructed explicit analytic solutions in $f(R)$ and hybrid metric-Palatini gravity.

Provided a geometric criterion for constraining free functions in scalar-tensor theories.

Abstract

We implement the Einsenhart-Duval lift in scalar-tensor gravity as a means to construct integrable cosmological models and analytic cosmological solutions. Specifically, we employ a geometric criterion to constrain the free functions of the scalar-tensor theory such that the field equations can be written in the equivalent form of linear equations. This geometric linearization is achieved by the introduction of an extended minisuperspace description. The results are applied to construct analytic solutions in modified theories of gravity such as the $f\left( R\right) $-theory and the hybrid metric-Palatini $f\left( \mathcal{R}\right) $-gravity.