K-Inflation in Noncommutative Space-Time
  The power spectra of the scalar and tensor perturbations in the
noncommutative k-inflation model are calculated in this paper. In this model,
all the modes created when the stringy space-time uncertainty relation is
satisfied are generated inside the sound/Hubble horizon during inflation for
the scalar/tensor perturbations. It turns out that a linear term describing the
noncommutative space-time effect contributes to the power spectra of the scalar
and tensor perturbations. Confronting the general noncommutative k-inflation
model with latest results from \textit{Planck} and BICEP2, and taking $c_S$ and
$\lambda$ as free parameters, we find that it is well consistent with
observations. However, for the two specific models, i.e. the tachyon and DBI
inflation models, it is found that the DBI model is not favored, while the
tachyon model lies inside the $1\sigma$ contour, if the e-folds number is
assumed to be around $50\sim60$.
