Abstract |
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[eng] The advent of explicit Dirac-Born-Infeld (DBI) inflationary models within
string theory has drawn renewed interest to the cosmological role of unusual
scalar field dynamics, usually referred to as k-inflation. In this situation,
the standard method used to determine the behavior of cosmological
perturbations breaks down. We present a generic method, based on the uniform
approximation, to analytically derive the power spectra of scalar and tensor
perturbations. For this purpose, a simple hierarchy of parameters, related to
the sound speed of the cosmological fluctuations and its successive
derivatives, is introduced in a k-inflation analogue of the Hubble flow
functions. The scalar spectral index and its running are obtained up to next to
next to leading order for all k-inflationary models. This result relies on the
existence of a well-motivated initial state, which is not trivial in the
present context: having the wavelength of the Fourier mode smaller than the
sonic horizon is indeed not enough and some conditions on the dynamics of the
sound speed are also required. Our method is then applied to various models
encountered in the literature. After deriving a generic slow-roll trajectory
valid for any DBI model, simple formulae for the cosmological observables are
obtained. In particular, the running, as the spectral index, for the so-called
UV and IR brane inflationary models is found to be uniquely determined by the
't Hooft coupling. Finally, the accuracy of these cosmological predictions is
assessed by comparing the analytical approximations with exact numerical
integrations.
Comment: 21 pages, 9 figures, uses RevTeX. References added, misprints
corrected, matches published version |