Coupling the Inflationary Sector to Matter

TL;DR

This paper demonstrates how matter fields can be coupled to an inflationary supergravity sector without disrupting inflation, ensuring stability and avoiding tachyons, especially in models with flat Kahler potentials.

Contribution

It proves conditions under which matter fields do not affect inflation and remain stable in supergravity models with flat Kahler potentials and quadratic superpotentials.

Findings

Matter fields do not affect inflationary dynamics under certain conditions.

No tachyons appear in the matter sector during and after inflation.

Matter masses are above the Hubble scale during inflation.

Abstract

We describe the coupling of matter fields to an inflationary sector of supergravity, the inflaton $\Phi$ and a stabilizer $S$, in models where the Kahler potential has a flat inflaton direction. Such models include, in particular, advanced versions of the hyperbolic $\alpha$-attractor models with a flat inflaton direction Kahler potential, providing a good fit to the observational data. If the superpotential is at least quadratic in the matter fields $U^{i}$, with restricted couplings to the inflaton sector, we prove that under certain conditions: i) The presence of the matter fields does not affect a successful inflationary evolution. ii) There are no tachyons in the matter sector during and after inflation. iii) The matter masses squared are higher than $3H^2$ during inflation. The simplest class of theories satisfying all required conditions is provided by models with a flat direction Kahler potential, and with the inflaton $\Phi$ and a stabilizer $S$ belonging to a hidden sector, so that matter fields have no direct coupling to the inflationary sector in the Kahler potential and in the superpotential.