de Sitter space and the equivalence between f(R) and scalar-tensor gravity

TL;DR

This paper demonstrates that metric f(R) gravity is fully equivalent to scalar-tensor theories with zero Brans-Dicke parameter for de Sitter space perturbations, clarifying stability conditions and challenging previous assumptions.

Contribution

It establishes the complete equivalence between metric f(R) gravity and scalar-tensor theories for de Sitter perturbations when f'' is non-zero.

Findings

Metric f(R) gravity is equivalent to scalar-tensor theories for de Sitter perturbations.

Stability conditions for de Sitter space are consistent across these theories.

Contradicts previous expectations about the limitations of this equivalence.

Abstract

It is shown that, when f'' is non-vanishing, metric f(R) gravity is completely equivalent to a scalar-tensor theory (with zero Brans-Dicke parameter) with respect to perturbations of de Sitter space, contrary to previous expectations. Moreover, the stability conditions of de Sitter space with respect to homogeneous and inhomogeneous perturbations coincide in most scalar-tensor theories, as is the case in metric f(R) gravity.