  Inflationary models within string theory exhibit unusual scalar field
dynamics involving non-minimal kinetic terms and generically referred to as
k-inflation. In this situation, the standard slow-roll approach used to
determine the behavior of the primordial cosmological perturbations cannot
longer be used. We present a generic method, based on the uniform
approximation, to analytically derive the primordial power spectra of scalar
and tensor perturbations. At leading order, the scalar spectral index, its
running and the tensor-to-scalar ratio are modified by the new dynamics. We
provide their new expression, correct previous results at next-to-leading order
and clarify the definition of what is the tensor-to-scalar ratio when the sound
horizon and Hubble radius are not the same. Finally, we discuss the constraints
the parameters encoding the non-minimal kinetic terms have to satisfy, such as
the sound speed and the energy scale of k-inflation, in view of the fifth year
Wilkinson Microwave Anisotropy Probe (WMAP5) data.
