Gravitational inflaton decay and the hierarchy problem

Abstract

We study implications of the large-$N$ species solution to the hierarchy problem, proposed by G. Dvali, for reheating of the Universe after inflation. Dvali's proposal contains additional $N\ensuremath{\sim}{10}^{32}{Z}_{2}$-conserved quantum fields beyond the standard model particles with mass $\ensuremath{\sim}1\text{ }\text{ }\mathrm{TeV}$, which weaken gravity by a factor of $1/N$, and thus explain the hierarchy between the Plank scale and the electroweak scale. We show that, in this scenario, the decay rates of inflaton fields through gravitational decay channels are enhanced by a factor of $N$, and thus they decay into $N$ species of the quantum fields very efficiently, in the limit that quantum gravity effects are unimportant for the gravitational decay rate. In order not to violate energy conservation or over-reheat the Universe, inflaton mass, vacuum expectation value of inflaton, or nonminimal gravitational coupling should be tightly fine-tuned. Our conclusion holds even when the gravitational decay is prohibited by some symmetry of the theory; the Universe may still be over-reheated via annihilation of inflatons, if the number density of inflaton quanta is greater than the critical value.