Inflation with $0 \leq c_{\rm s} \leq 1$

TL;DR

This paper introduces a unified inflationary model that smoothly transitions between different sound speed regimes, including the challenging $c_s o 0$ limit, by incorporating higher derivative terms, with implications for primordial black hole formation.

Contribution

It presents a novel single-field inflationary framework unifying slow-roll and ghost inflation through higher derivative corrections, enabling a consistent approach to the entire $c_s$ range.

Findings

Achieves a smooth transition between $c_s$ regimes without instabilities.

Provides a self-consistent model for $c_s o 0$ inflation.

Discusses potential for primordial black hole formation.

Abstract

We investigate a novel single field inflationary scenario which allows a transition between a slow-roll k-inflation with $c_{\rm s}$ of order unity and a ghost inflation with $ c_{\rm s} \simeq 0$, where $ c_{\rm s}$ is the sound speed for the curvature perturbations. We unify the two phases smoothly by appropriately taking into account a higher derivative scordatura term, which is always there from the effective field theory point of view but which becomes important only in the $c_{\rm s} \simeq 0$ regime. The model achieves the whole range of $0 \leq c_{\rm s} \leq 1$ avoiding strong coupling and gradient instability, and allows us to access the $c_{\rm s} \simeq 0$ regime in a self-consistent manner. We also discuss implications to the formation of primordial black holes.