Gravitational production of scalar dark matter

We investigate the gravitational production of scalar dark matter particles during the inflationary and reheating epochs. The oscillatory behavior of the curvature scalar $R$ during the reheating phase generates two different enhancement mechanisms in the particle production. On the one hand, as it has been already discussed in previous works, it induces tachyonic instabilities in the field which are the dominant enhancement mechanism for light masses. On the other hand, we have found that it also provokes a resonant effect in the ultraviolet region of the spectrum which becomes dominant for masses in the range $10^9\,{\rm GeV}$ to $10^{13}\,{\rm GeV}$. We have developed an analytical approximation to describe this resonance effect and its consequences on the ultraviolet regime. Once we have calculated the theoretical gravitational production, we constrain the possible values of the phenomenological field parameters to be considered as a dark matter candidate. We do so by comparing the theoretically predicted abundance with the observed one and ensuring that the theoretical prediction does not lead to overproduction. In particular, we find that there is a region of intermediate masses that is forbidden as they would lead to overproduction.