The effective field theory (EFT) of cosmological perturbations is a useful framework to deal with the low-energy degrees of freedom present for inflation and dark energy. We review the EFT for modified gravitational theories by starting from the most
general action in unitary gauge that involves the lapse function and the three-dimensional geometric scalar quantities appearing in the Arnowitt-Deser-Misner (ADM) formalism. Expanding the action up to quadratic order in the perturbations and imposing conditions for the elimination of spatial derivatives higher than second order, we obtain the Lagrangian of curvature perturbations and gravitational waves with a single scalar degree of freedom. The resulting second-order Lagrangian is exploited for computing the scalar and tensor power spectra generated during inflation. We also show that the most general scalar-tensor theory with second-order equations of motion-Horndeski theory-belongs to the action of our general EFT framework and that the background equations of motion in Horndeski theory can be conveniently expressed in terms of three EFT parameters. Finally we study the equations of matter density perturbations and the effective gravitational coupling for dark energy models based on Horndeski theory, to confront the models with the observations of large-scale structures and weak lensing.
We study chaotic inflation in the context of modified gravitational theories. Our analysis covers models based on (i) a field coupling $omega(phi)$ with the kinetic energy $X$ and a nonmimimal coupling $zeta phi^{2} R/2$ with a Ricci scalar $R$, (ii)
Brans-Dicke (BD) theories, (iii) Gauss-Bonnet (GB) gravity, and (iv) gravity with a Galileon correction. Dilatonic coupling with the kinetic energy and/or negative nonminimal coupling are shown to lead to compatibility with observations of the Cosmic Microwave Background (CMB) temperature anisotropies for the self-coupling inflaton potential $V(phi)=lambda phi^{4}/4$. BD theory with a quadratic inflaton potential, which covers Starobinskys $f(R)$ model $f(R)=R+R^{2}/(6M^{2})$ with the BD parameter $omega_{BD}=0$, gives rise to a smaller tensor-to-scalar ratio for decreasing $omega_{BD}$. In the presence of a GB term coupled to the field $phi$, we express the scalar/tensor spectral indices $n_{s}$ and $n_{t}$ as well as the tensor-to-scalar ratio $r$ in terms of two slow-roll parameters and place bounds on the strength of the GB coupling from the joint data analysis of WMAP 7yr combined with other observations. We also study the Galileon-like self-interaction $Phi(phi) X squarephi$ with exponential coupling $Phi(phi) propto e^{muphi}$. Using a CMB likelihood analysis we put bounds on the strength of the Galileon coupling and show that the self coupling potential can in fact be made compatible with observations in the presence of the exponential coupling with $mu>0$.
We study constraints on f(R) dark energy models from solar system experiments combined with experiments on the violation of equivalence principle. When the mass of an equivalent scalar field degree of freedom is heavy in a region with high density, a
spherically symmetric body has a thin-shell so that an effective coupling of the fifth force is suppressed through a chameleon mechanism. We place experimental bounds on the cosmologically viable models recently proposed in literature which have an asymptotic form f(R)=R-lambda R_c [1-(R_c/R)^{2n}] in the regime R >> R_c. From the solar-system constraints on the post-Newtonian parameter gamma, we derive the bound n>0.5, whereas the constraints from the violations of weak and strong equivalence principles give the bound n>0.9. This allows a possibility to find the deviation from the LambdaCDM cosmological model. For the model f(R)=R-lambda R_c(R/R_c)^p with 0<p<1 the severest constraint is found to be p<10^{-10}, which shows that this model is hardly distinguishable from the LambdaCDM cosmology.
