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f(R) Theories Of Gravity

Thomas P. Sotiriou, Valerio Faraoni

Abstract

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories which include higher order curvature invariants, and specifically the particular class of f(R) theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. We review here f(R) theories of gravity in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented -- metric, Palatini and metric-affine -- and the following topics are discussed: motivation; actions, field equations and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; astrophysical applications.

f(R) Theories Of Gravity

Abstract

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories which include higher order curvature invariants, and specifically the particular class of f(R) theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. We review here f(R) theories of gravity in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented -- metric, Palatini and metric-affine -- and the following topics are discussed: motivation; actions, field equations and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; astrophysical applications.

Paper Structure

This paper contains 43 sections, 199 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Historical
  3. Contemporary Motivation
  4. $f(R)$ theories as toy theories
  5. Actions and field equations
  6. Metric formalism
  7. Palatini formalism
  8. Metric-affine formalism
  9. Preliminaries
  10. Field Equations
  11. Equivalence with Brans--Dicke theory and classification of theories
  12. Metric formalism
  13. Palatini formalism
  14. Classification
  15. Why $f(R)$ gravity then?
  16. ...and 28 more sections

Figures (1)

  • Figure 1: Classification of $f(R)$ theories of gravity and equivalent Brans--Dicke theories. The flowchart shows the list of assumptions that are needed to arrive to the various versions of $f(R)$ gravity and GR beginning from the the general $f(R)$ action. It also includes the equivalent Brans--Dicke classes. Taken from Sotiriou:2006hs.