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 \mbox { GeV } , corresponding to gravity-mediated supersymmetry breaking , this leads to the well-known bound \gamma T _ { R } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt% \hbox { $ < $ } } 10 ^ { 9 } \mbox { 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 _ { R } if supersymmetry breaking is gravity-mediated .