The Cauchy problem of f(R) gravity

TL;DR

This paper investigates the initial value problem in f(R) gravity theories, showing that metric f(R) gravity is well-posed with matter, while Palatini f(R) gravity faces formulation issues.

Contribution

It clarifies the well-posedness of the Cauchy problem in metric and Palatini f(R) gravity using their equivalence to Brans-Dicke theory.

Findings

Metric f(R) gravity is well-posed with matter.

Palatini f(R) gravity's Cauchy problem is not well-formulated.

The analysis uses the dynamical equivalence to Brans-Dicke gravity.

Abstract

The initial value problem of metric and Palatini f(R)gravity is studied by using the dynamical equivalence between these theories and Brans-Dicke gravity. The Cauchy problem is well-formulated for metric f(R)gravity in the presence of matter and well-posed in vacuo. For Palatini f(R)gravity, instead, the Cauchy problem is not well-formulated.