"f (R) Theories"
by
Antonio De Felice and Shinji Tsujikawa
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Abstract
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
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
References
Footnotes
Figures
Tables