Modified gravity and Space-Time-Matter theory

TL;DR

This paper explores the relationship between $f(R)$ gravity theories and 5D Space-Time-Matter models, demonstrating how geometric interpretations in higher dimensions can explain dark energy and cosmic acceleration.

Contribution

It establishes a correspondence between $f(R)$ theories and 5D STM models, providing a method to interpret 4D induced effects from 5D geometry, including explicit examples and cosmological implications.

Findings

Demonstrates the correspondence between $f(R)$ gravity and 5D STM theories.

Shows how arbitrary functions in 5D solutions relate to 4D cosmological models.

Analyzes accelerated expansion and dark energy in a 5D Ricci-flat universe.

Abstract

The correspondence between $f(R)$ theories of gravity and model theories explaining induced dark energy in a 5D Ricci-flat universe, known as the Space-Time-Matter theory (STM), is studied. It is shown that such correspondence may be used to interpret the four dimensional expressions, induced from geometry in 5D STM theories, in terms of the extra terms appearing in $f(R)$ theories of gravity. The method is demonstrated by providing an explicit example in which a given $f(R)$ is used to predict the properties of the corresponding 5D Ricci-flat universe. The accelerated expansion and the induced dark energy in a 5D Ricci-flat universe characterized by a big bounce is studied and it is shown that an arbitrary function $\mu(t)$ in the 5D solutions can be rewritten, in terms of the redshift $z$, as a new arbitrary function $F(z)$ which corresponds to the 4D curvature quintessence models.