The abundance of moduli, modulini and gravitinos produced by the vacuum fluctuation

TL;DR

This paper examines how vacuum fluctuations produce moduli, modulini, and gravitinos after inflation, affecting bounds on reheat temperature and potential dark matter candidates, with implications for supersymmetry breaking scenarios.

Contribution

It provides a detailed analysis of vacuum fluctuation production of these particles, confirming existing estimates and highlighting the impact on reheat temperature bounds and dark matter possibilities.

Findings

Vacuum-produced modulini and moduli are less abundant than thermal production.

Gravitino abundance from vacuum fluctuations can be significantly higher, tightening reheat temperature constraints.

In gauge-mediated SUSY breaking, gravitinos may serve as dark matter candidates.

Abstract

Moduli, modulini and the gravitino have gravitational-strength interactions, and thermal collisions after reheating create all of them with roughly the same abundance. With their mass of order $100\GeV$, corresponding to gravity-mediated supersymmetry breaking, this leads to the well-known bound $\gamma T\sub R\lsim 10^9\GeV$ on the reheat temperature, where $\gamma\leq 1$ is the entropy dilution factor. The vacuum fluctuation also creates these particles, with abundance determined by the solution of the equation for the mode function. Taking the equation in each case to be the one corresponding to a free field, we consider carefully the behaviour of the effective mass during the crucial era after inflation. It may have a rapid oscillation, which does not however affect the particle abundance. Existing estimates are confirmed; the abundance of modulini and (probably) of moduli created from the vacuum is less than from thermal collisions, but the abundance of gravitinos may be much bigger, leading to a tighter bound on $T\sub R$ if supersymmetry breaking is gravity-mediated. It is noted that in the case of gauge-mediated supersymmetry breaking, the abundance of the gravitino may be sufficient to make it a dark matter candidate.