Non-minimally coupled hybrid inflation

TL;DR

This paper explores a non-minimally coupled hybrid inflation model, classifying inflation types, analyzing their dynamics, and predicting the resulting curvature perturbation spectra, with numerical confirmation of spectral transitions.

Contribution

It introduces a hybrid inflation model with nonminimal coupling, analyzing different inflation types and their spectral signatures, including numerical validation of spectral transitions.

Findings

Inflation can be classified into two types based on termination mechanism.

Spectral index varies from red to blue depending on inflation type and region.

Numerical simulations confirm the transition of curvature perturbation spectra.

Abstract

We discuss the hybrid inflation model where the inflaton field is nonminimally coupled to gravity. In the Jordan frame, the potential contains $\phi^4$ term as well as terms in the original hybrid inflation model. In our model, inflation can be classified into the type (I) and the type (II). In the type (I), inflation is terminated by the tachyonic instability of the waterfall field, while in the type (II) by the violation of slow-roll conditions. In our model, the reheating takes place only at the true minimum and even in the case (II) finally the tachyonic instability occurs after the termination of inflation. For a negative nonminimal coupling, inflation takes place in the vacuum-dominated region, in the large field region, or near the local minimum/maximum. Inflation in the vacuum dominated region becomes either the type (I) or (II), resulting in blue or red spectrum of the curvature perturbations, respectively. Inflation around the local maximum can be either the type (I) or the type (II), which results in the red spectrum of the curvature perturbations, while it around the local minimum must be the type (I), which results in the blue spectrum. In the large field region, to terminate inflation, potential in the Einstein frame must be positively tilted, always resulting in the red spectrum. We then numerically solve the equations of motion to investigate the whole dynamics of inflaton and confirm that the spectrum of curvature perturbations changes from red to blue ones as scales become smaller.