The Effect of Varying Sound Velocity on Primordial Curvature Perturbations

Abstract

We study the effects of sudden change in the sound velocity on primordial curvature perturbation spectrum in inflationary cosmology, assuming that the background evolution satisfies the slow-roll condition throughout. It is found that the power spectrum acquires oscillating features which are determined by the ratio of the sound speed before and after the transition and the wavenumeber which crosses the sound horizon at the transition, and their analytic expression is given. In some values of those parameters, the oscillating primordial power spectrum can better fit the observed Cosmic Microwave Background temperature anisotropy power spectrum than the simple power-law power spectrum, although introduction of such a new degree of freedom is not justified in the context of Akaike's Information Criterion.Subject Index: 400, 436, 440, 442 * ) As discussed in Appendix A, this is not the case in the curvaton scenario.

Preinflationary primordial perturbations

“…Actually, for scalar fields, c 2 s may also be different from 1. The effects of varying sound speed on primordial perturbations has been studied; see, e.g., [75], [76]. But as long as c 2 s is a positive constant during each phase, our result is not qualitatively altered.…”

Searching for primordial localized features with CMB and LSS spectra

“…The effect of a variable speed of sound has also been analyzed both in the power spectrum [4,47,48] and bispectrum [4,27,49]. Similar studies of a power spectrum [15,26,[50][51][52] and bispectrum [15,52,53] have also been done for models with sudden variations. In addition, the Planck collaboration searched for features in the CMB bispectrum for a number of theoretically motivated templates [3], including oscillatory templates.…”

Correlating correlation functions of primordial perturbations

“…Likewise, in the right panel of Fig. 1 we show the case where c −2 s exhibits a top-hat change [24] from 1 to 1.1 for limited e-folds 0.15.…”