The Cauchy problem for f(R)-gravity: an overview

TL;DR

This paper reviews the initial value problem in f(R) gravity theories, comparing metric and metric-affine formulations, and discusses conditions for their mathematical well-posedness and physical viability.

Contribution

It provides a comprehensive overview of the Cauchy problem in f(R) gravity, highlighting differences from General Relativity and analyzing criteria for model viability.

Findings

Comparison of metric and metric-affine formulations

Analysis of conformal transformations and scalar fields

Criteria for the physical viability of f(R) models

Abstract

We review the Cauchy problem for f(R) theories of gravity, in metric and metric-affine for- mulations, pointing out analogies and differences with respect to General Relativity. The role of conformal transformations, effective scalar fields and sources in the field equations is discussed in view of the well-posedness of the problem. Finally, criteria of viability of the f(R)-models are considered according to the various matter fields acting as sources.