# Dirac-Born-Infeld and k-inflation: the CMB anisotropies from string theory

## TL;DR

This paper develops an analytical method to compute primordial perturbations in string theory-based k-inflation models, refining previous results and analyzing observational constraints from WMAP5 data.

## Contribution

It introduces a uniform approximation technique for deriving power spectra in k-inflation, correcting earlier results and clarifying the tensor-to-scalar ratio definition.

## Key findings

- Modified expressions for spectral index, running, and tensor-to-scalar ratio.
- Corrected next-to-leading order results for primordial spectra.
- Constraints on sound speed and energy scale from WMAP5 data.

## Abstract

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.