Power spectra and spectral indices of $k$-inflation: high-order corrections

Abstract

$k$-inflation represents the most general single-field inflation, in which the perturbations usually obey an equation of motion with a time-dependent sound speed. In this paper, we study the observational predictions of the $k$-inflation by using the high-order uniform asymptotic approximation method. We calculate explicitly the slow-roll expressions of the power spectra, spectral indices, and running of the spectral indices for both the scalar and tensor perturbations. These expressions are all written in terms of the Hubble and sound speed flow parameters. It is shown that the previous results obtained by using the first-order uniform asymptotic approximation have been significantly improved by the high-order corrections of the uniform asymptotic approximations. Furthermore, we also check our results by comparing them with the ones obtained by other approximation methods, including the Green's function method, WKB approximation, and improved WKB approximation, and find the relative errors.

Typos are also corrected. Phys. Rev. D90, 103517 (2014). arXiv admin note: text overlap with arXiv:1405.5301

References in corpus (4)

• K-inflationary Power Spectra in the Uniform Approximation
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• Computation of inflationary cosmological perturbations in the power-law inflationary model using the phase-integral method
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• Inflationary Cosmology with Quantum Gravitational Effects and the Swampland Conjectures
• Effects of high-order operators in non-relativistic Lifshitz holography
• Stable initial conditions and analytical investigations of cosmological perturbations in a modified loop quantum cosmology