Living Reviews in Relativity

"f (R) Theories"
Antonio De Felice and Shinji Tsujikawa  

Hide Subsections

1 Introduction
2 Field Equations in the Metric Formalism
2.1 Equations of motion
2.2 Equivalence with Brans–Dicke theory
2.3 Conformal transformation
3 Inflation in f (R) Theories
3.1 Inflationary dynamics
3.2 Dynamics in the Einstein frame
3.3 Reheating after inflation
4 Dark Energy in f (R) Theories
4.1 Dynamical equations
4.2 Viable f (R) dark energy models
4.3 Equation of state of dark energy
5 Local Gravity Constraints
5.1 Linear expansions of perturbations in the spherically symmetric background
5.2 Chameleon mechanism in f (R) gravity
6 Cosmological Perturbations
6.1 Perturbation equations
6.2 Gauge-invariant quantities
7 Perturbations Generated During Inflation
7.1 Curvature perturbations
7.2 Tensor perturbations
7.3 The spectra of perturbations in inflation based on f (R) gravity
7.4 The Lagrangian for cosmological perturbations
8 Observational Signatures of Dark Energy Models in f (R) Theories
8.1 Matter density perturbations
8.2 The impact on large-scale structure
8.3 Non-linear matter perturbations
8.4 Cosmic Microwave Background
9 Palatini Formalism
9.1 Field equations
9.2 Background cosmological dynamics
9.3 Matter perturbations
9.4 Shortcomings of Palatini f (R) gravity
10 Extension to Brans–Dicke Theory
10.1 Brans–Dicke theory and the equivalence with f (R) theories
10.2 Cosmological dynamics of dark energy models based on Brans–Dicke theory
10.3 Local gravity constraints
10.4 Evolution of matter density perturbations
11 Relativistic Stars in f (R) Gravity and Chameleon Theories
11.1 Field equations
11.2 Constant density star
11.3 Relativistic stars in metric f (R) gravity
12 Gauss–Bonnet Gravity
12.1 Lovelock scalar invariants
12.2 Ghosts
12.3 f(𝒢 ) gravity
12.4 Gauss–Bonnet gravity coupled to a scalar field
13 Other Aspects of f (R) Theories and Modified Gravity
13.1 Weak lensing
13.2 Thermodynamics and horizon entropy
13.3 Curing the curvature singularity in f (R) dark energy models, unified models of inflation and dark energy
13.4 f (R) theories in extra dimensions
13.5 Vainshtein mechanism
13.6 DGP model
13.7 Special symmetries
14 Conclusions
15 Acknowledgements
Open References References