Abstract
We study the K-Inflation models where the inflaton field has non-canonical 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 the MODECODE (proposed by Mortonson et al.) 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 DBI type kinetic term, lesser gravity waves are produced as one approaches more towards 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 DBI type kinetic term to be consistent with WMAP data.
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