
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 
Gaugeinvariant 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 largescale structure 

8.3 
Nonlinear
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 