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Chaotic inflation in modified gravitational theories

We study chaotic inflation in the context of modified gravitational theories. Our analysis covers models based on (i) a field coupling $ω(ϕ)$ with the kinetic energy $X$ and a nonmimimal coupling $ζϕ^{2} R/2$ 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 $V(ϕ)=λϕ^{4}/4$. BD theory with a quadratic inflaton potential, which covers Starobinsky's $f(R)$ model $f(R)=R+R^{2}/(6M^{2})$ with the BD parameter $ω_{BD}=0$, gives rise to a smaller tensor-to-scalar ratio for decreasing $ω_{BD}$. In the presence of a GB term coupled to the field $ϕ$, 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 $Φ(ϕ) X \squareϕ$ with exponential coupling $Φ(ϕ) \propto e^{μϕ}$. 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 $μ>0$.