Curvature perturbation spectrum from false vacuum inflation

TL;DR

This paper calculates the curvature perturbation spectrum during false vacuum inflation, revealing a steeply blue spectrum with spectral index n_R=4, by directly evaluating quantum correlations in a trapping potential scenario.

Contribution

It provides the first explicit calculation of the curvature perturbation power spectrum during false vacuum inflation with a trapping mechanism.

Findings

The spectrum is steeply blue with spectral index n_R=4.

Quantum two-point correlation functions are used for the calculation.

The results clarify the nature of perturbations during false vacuum stages.

Abstract

In the inflationary cosmology it occurs frequently that the inflaton field is trapped in a local, transient minimum with non-zero vacuum energy. The difficulty regarding the curvature perturbation produced during such a stage is that classically the inflaton does not move so that the comoving hypersurfaces are not well defined at linear order in the scalar field perturbation. In this paper, assuming a mechanism of trapping which resembles a high temperature correction to the potential, we explicitly calculate for the first time the resulting power spectrum of the curvature perturbation by evaluating the quantum two-point correlation function directly. The spectrum is steeply blue with the spectral index n_R = 4.