Nonminimal Superheavy Dark Matter

We investigate the gravitational production of superheavy scalar fields with nonminimal coupling during and after inflation. We derive analytical approximations using the mode function solution in a de Sitter background and also apply the steepest descent method. We study both positive and negative nonminimal couplings and show that their comoving number density spectra behave differently in the short and long wavelength regimes. We numerically compute the comoving number density spectra and dark matter abundance for a broad range of superheavy spectator fields exceeding the Hubble scale during inflation, with $m_{\chi} > H_I$, and nonminimal couplings ranging from $-300 \leq \xi \leq 300$. When computing the allowed dark matter parameter space, we impose the maximum reheating temperature constraint, the Big Bang nucleosynthesis constraint, and the isocurvature constraint. We show that the presence of a positive or negative coupling $\xi$ can expand the parameter space up to $3$ orders of magnitude above the Hubble inflationary scale, allowing such dark matter candidates to be as heavy as $\sim 10^{16} \, \rm{GeV}$ in the Starobinsky model of inflation.