Growth of power spectrum due to decrease of sound speed during inflation

Abstract

We study the amplification of the curvature perturbations due to a small sound speed and find that its origin is different completely from that due to the ultraslow-roll inflation. This is because when the sound speed is very small the enhancement of the power spectrum comes from the fact that the curvature perturbations at the scales smaller than the cosmic microwave background (CMB) scale becomes scale-variant, rather than growing that leads to the amplification of the curvature perturbations during the ultraslow-roll inflation. At large scales the power spectrum of the curvature perturbations remains to be scale invariant, which is consistent with the CMB observations, and then it will have a transient $k^2$ growth and finally approach a $k^4$ growth as the scale becomes smaller and smaller. Thus the power spectrum can be enhanced to generate a sizable amount of primordial black holes. Furthermore, when the high order correction in the dispersion relation of the curvature perturbations is considered the growth of the power spectrum of the curvature perturbations has the same origin as that in the case without this correction.

arXiv comment11 pages, 1 figure. three references added

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• Generation of primordial black holes from an inflation model with modified dispersion relation
• Primordial Black Hole Formation in Non-Standard Post-Inflationary Epochs
• Primordial Black Holes Dark Matter and Secondary Gravitational Waves from Warm Higgs-G Inflation
• Impact of radiation from primordial black holes on the 21-cm angular-power spectrum in the dark ages
• DESIgning concordant distances in the age of precision cosmology: the impact of density fluctuations
• Frame-Dependence of the Hamilton-Jacobi Formalism for Inflation and Reheating in Non-Minimal Gravity
• Probing the Perturbative Reheating History of Decaying Oscillatory Inflation with ACT Constraints
• Primordial black holes and scalar induced gravitational waves from sound speed resonance in non-minimal derivative coupling inflation model