Inflation and High-Scale Supersymmetry with an EeV Gravitino

TL;DR

This paper explores a minimal supersymmetry model with an EeV-scale gravitino, demonstrating that inflation and reheating are compatible with a very high supersymmetry breaking scale, resulting in gravitino dark matter.

Contribution

It shows that inflation can occur with a supersymmetry breaking scale above the inflaton mass in a no-scale Starobinsky-like model, and constrains gravitino dark matter mass range.

Findings

Inflation is compatible with high-scale supersymmetry breaking.

Reheating is driven by gravitational coupling to Higgs doublets.

Gravitino dark matter mass is constrained between 0.1 EeV and 1000 EeV.

Abstract

We consider inflation and supersymmetry breaking in the context of a minimal model of supersymmetry in which the only "low" energy remnant of supersymmetry is the gravitino with a mass of order an EeV. In this theory, the supersymmetry breaking scale is above the inflaton mass, m ~ 3 x 10^{13} GeV, as are all sfermion and gaugino masses. In particular, for a no-scale formulation of Starobinsky-like inflation using the volume modulus T, we show that inflation can be accommodated even when the supersymmetry breaking scale is very large. Reheating is driven through a gravitational coupling to the two Higgs doublets and is enhanced by the large mu-parameter. This leads to gravitino cold dark matter where the mass is constrained to be in the range 0.1 EeV $\lesssim m_{3/2} \lesssim 1000$ EeV.