Correspondence between modified gravity and 5D Ricci-flat cosmologies

TL;DR

This paper explores the connection between $f(R)$ modified gravity and 5D Ricci-flat cosmologies, demonstrating how the Hubble parameter in $f(R)$ models relates to metric functions in higher-dimensional theories, with implications for late-time cosmic acceleration.

Contribution

It establishes a correspondence between $f(R)$ gravity and 5D Ricci-flat cosmologies, providing a new perspective on modeling dark energy in higher-dimensional frameworks.

Findings

Hubble parameter in $f(R)$ gravity linked to 5D metric functions

Specific model consistent with late-time acceleration

Demonstrates equivalence between two dark energy descriptions

Abstract

We study the correspondence between two theoretical frameworks for describing dark energy, $f(R)$ gravity and higher-dimensional Space-Time-Matter (STM) or induced-matter theory. We show that the Hubble expansion parameter in $f(R)$ gravity can be associated with a combination of metric functions in STM theory, and consider a specific example whose properties are consistent with late-time acceleration.