Inflationary signatures of single-field models beyond slow-roll

TL;DR

This paper explores the unique inflationary signatures of all single-field models without ghost instabilities, especially when the universe's expansion deviates from slow-roll, revealing complex bispectrum behaviors.

Contribution

It introduces a scale-invariant approximation framework to analyze non-slow-roll single-field inflation models and computes their scalar propagator and bispectrum with next-order corrections.

Findings

Bispectrum shape and scale-dependence are highly non-trivial outside slow-roll.

Explicit models show deviations from standard slow-roll predictions.

Results support compatibility with current cosmological observations.

Abstract

If the expansion of the early Universe was not close to de Sitter, the statistical imprints of the primordial density perturbation on the cosmic microwave background can be quite different from those derived in slow-roll inflation. In this paper we study the inflationary signatures of all single-field models which are free of ghost-like instabilities. We allow for a rapid change of the Hubble parameter and the speed of sound of scalar fluctuations, in a way that is compatible with a nearly scale-invariant spectrum of perturbations, as supported by current cosmological observations. Our results rely on the scale-invariant approximation, which is different from the standard slow-roll approximation. We obtain the propagator of scalar fluctuations and compute the bispectrum, keeping next-order corrections proportional to the deviation of the spectral index from unity. These theories offer an explicit example where the shape and scale-dependences of the bispectrum are highly non-trivial whenever slow-roll is not a good approximation.