New K\"ahler invariant Fayet-Iliopoulos terms in supergravity and cosmological applications

TL;DR

This paper introduces a new class of K"ahler invariant Fayet-Iliopoulos terms in supergravity, enabling novel inflation models compatible with observations and offering mechanisms to fix the gravitino mass.

Contribution

It generalizes recent FI-term constructions, creating models with tunable vacuum energy and gauged axionic shift symmetry within no-scale supergravity.

Findings

Inflation models compatible with CMB data.

Vacuum energy at the minimum can be finely tuned.

Gauging of axionic shift symmetry leads to massive U(1).

Abstract

Recently, a new type of constant Fayet-Iliopoulos (FI) terms was introduced in $\mathcal{N}=1$ supergravity, which do not require the gauging of the $R$-symmetry. We revisit and generalise these constructions, building a new class of K\"ahler invariant FI terms parametrised by a function of the gravitino mass as functional of the chiral superfields, which is then used to describe new models of inflation. They are based on a no-scale supergravity model of the inflaton chiral multiplet, supplemented by an abelian vector multiplet with the new FI-term. We show that the inflaton potential is compatible with the CMB observational data, with a vacuum energy at the minimum that can be tuned to a tiny positive value. Finally, the axionic shift symmetry can be gauged by the $U(1)$ which becomes massive. These models offer a mechanism for fixing the gravitino mass in no-scale supergravities, that corresponds to a flat direction of the scalar potential in the absence of the new FI-term; its origin in string theory is an interesting open problem.