The dynamics of generalized Palatini Theories of Gravity

TL;DR

This paper investigates the behavior of generalized Palatini theories of gravity, demonstrating that the algebraic elimination of the connection is specific to f(R) actions and does not extend to more general curvature invariants, clarifying misconceptions in recent literature.

Contribution

It clarifies that the algebraic elimination of the connection is unique to f(R) theories and not applicable to more general curvature actions, correcting recent claims.

Findings

Algebraic elimination of the connection is specific to f(R) theories.

This property does not hold for actions with other curvature invariants.

The paper resolves contradictions in recent literature regarding Palatini theories.

Abstract

It is known that in f(R) theories of gravity with an independent connection which can be both non-metric and non symmetric, this connection can always be algebraically eliminated in favour of the metric and the matter fields, so long as it is not coupled to the matter explicitly. We show here that this is a special characteristic of f(R) actions, and it is not true for actions that include other curvature invariants. This contradicts some recent claims in the literature. We clarify the reasons of this contradiction.