String duality transformations in $f(R)$ gravity from Noether symmetry approach

TL;DR

This paper explores how string theory dualities can be translated into $f(R)$ gravity models using Noether symmetry, leading to exact cosmological solutions and revealing parity-inversion dualities.

Contribution

It demonstrates a method to derive $f(R)$ gravity models from string theory dualities via Noether symmetry, providing new exact solutions.

Findings

String dualities can be mapped to $f(R)$ gravity models.

Exact cosmological solutions are obtained from duality considerations.

Duality transformations can be represented as parity inversions in certain cases.

Abstract

We select $f(R)$ gravity models that undergo scale factor duality transformations. As a starting point, we consider the tree-level effective gravitational action of bosonic String Theory coupled with the dilaton field. This theory inherits the Busher's duality of its parent String Theory. Using conformal transformations of the metric tensor, it is possible to map the tree-level dilaton-graviton string effective action into $f(R)$ gravity, relating the dilaton field to the Ricci scalar curvature. Furthermore, the duality can be framed under the standard of Noether symmetries and exact cosmological solutions are derived. Using suitable changes of variables, the string-based $f(R)$ Lagrangians are shown in cases where the duality transformation becomes a parity inversion.