Planck constraints on single-field inflation

We place observational constraints on slow-variation single-field inflationary models by carrying out the cosmological Monte Carlo simulation with the recent data of Planck combined with the WMAP large-angle polarization, baryon acoustic oscillations, and Atacama Cosmology Telescope/ South Pole Telescope temperature data. Our analysis covers a wide variety of models with second-order equations of motion, including potential-driven slow-roll inflation, nonminimally coupled models, running kinetic couplings, Brans-Dicke theories, potential-driven Galileon inflation, field-derivative couplings to the Einstein tensor, and k-inflation. In the presence of running kinetic exponential couplings, covariant Galileon terms, and field-derivative couplings, the tensor-to-scalar ratio of the self-coupling potential V( phi) = lambda phi(4)/4 gets smaller relative to that in standard slow-roll inflation, but the models lie outside the 1 sigma observational contour. We also show that k-inflation models can be tightly constrained by adding the bounds from the scalar non-Gaussianities. The small-field inflationary models with asymptotic flat Einstein-frame potentials in the regime phi >> M-p1 generally fit the data very well. These include the models such as Kahler-moduli inflation, nonminimally coupled Higgs inflation, and inflation in Brans-Dicke theories in the presence of the potential V(phi) =3M(2) d(phi - M-p1)(2)/4 with the Brans-Dicke parameter omega(BD) less than or similar to O(1) ( which covers the Starobinsky's model f(R) =R+ R-2/(6M(2)) as a special case).