f(R) Gravity and scalar-tensor theory

TL;DR

This paper explores the relationship between $f(R)$ gravity theories and scalar-tensor theories, focusing on the Palatini formalism, to understand when they are equivalent and the implications of such equivalence.

Contribution

It investigates the conditions under which $f(R)$ theories in the Palatini formalism are equivalent to scalar-tensor theories, extending previous metric formalism studies.

Findings

Identifies conditions for equivalence between $f(R)$ and scalar-tensor theories in Palatini formalism.

Analyzes implications of the equivalence for gravitational theories.

Provides insights into the theoretical foundations of modified gravity models.

Abstract

In the present paper we will investigate the relation between scalar-tensor theory and $f(R)$ theories of gravity. Such studies have been performed in the past for the metric formalism of $f(R)$ gravity; here we will consider mainly the Palatini formalism, where the metric and the connections are treated as independent quantities. We will try to investigate under which circumstances $f(R)$ theories of gravity are equivalent to scalar-tensor theory and examine the implications of this equivalence, when it exists.