WMAP constraints on k-inflation

We study the k-inflation models where the inflaton field has a noncanonical kinetic term. In particular, we consider the Dirac-Born-Infeld (DBI) form for the kinetic energy of the inflaton field. We consider quadratic and quartic potentials as well as the potential for the natural inflation. We use a modified version of MODECODE [M. J. Mortonson, H. V. Peiris, and R. Easther, Phys. Rev. D 83, 043505 (2011).] to calculate the power spectrum of the primordial perturbations generated by the inflaton field and subsequently use the WMAP7 results to constrain the models. Interestingly, with the DBI type kinetic term, less gravity waves are produced as one approaches scale invariance. This is true for all the potentials considered. Unlike the canonical case, this feature, in particular, helps the quartic (lambda phi(4)) potential with the DBI type kinetic term to be consistent with the WMAP data.