O(d,d) duality transformations in F(R) theories of gravity

TL;DR

This paper explores how O(d,d) duality transformations in bosonic string theory can be applied to f(R) gravity theories, revealing duality symmetries in cosmological models through a connection with string theory and Noether symmetries.

Contribution

It demonstrates the implementation of O(d,d) duality in f(R) gravity derived from string theory, linking duality symmetries with cosmological solutions.

Findings

f(R) Lagrangian exhibits Gasperini-Veneziano duality symmetry

Connection established between string dualities and extended gravity theories

Duality symmetry constrains the form of f(R) models in cosmology

Abstract

The argument of Hodge duality symmetry is introduced starting from the electromagnetic field. Introducing bosonic string theory, O(d,d) duality symmetry can be implemented when there exist d-symmetries, which allows one to write Hodge-dual fields. A tree-level effective gravitational action of bosonic string theory coupled with the dilaton field is considered. This theory inherits the Busher's duality of its parent string theory. The dilaton field can be recast into the Weyl's mode of the metric tensor in the Jordan frame. This maps the effective one-loop bosonic string theory of gravity into a Lagrangian of a f(R) function. Constraining this f(R)-Lagrangian on a FLRW metric and using Noether symmetries approach for extended theory of gravity, it is possible to show that the Lagrangian exibits a Gasperini-Veneziano duality symmetry.