Universality classes of sharp gravitational production of light particles

Abstract

We establish a classification of the gravitational production of light particles across sharp transitions connecting different asymptotic forms of the scale factor. A family of smooth scale factors with a transition duration $\Delta \eta$ is characterized by its regularity in the sharp-transition limit $\Delta \eta \to 0$, leading to three qualitatively different universality classes: $C^0$, $C^1$, and $C^2$-or-smoother. We find that the $C^0$ class exhibits a quadratic enhancement in the energy density of produced particles, $\rho \propto \Delta {\eta }^{-2}$, while the $C^1$ class shows a logarithmic enhancement, $\rho \propto \ln (1/\Delta \eta )$. No sharp-transition enhancement occurs for the $C^2$-or-smoother class. Using a specific $C^{\infty }$ model of the scale factor, we derive the energy density analytically and confirm both the predicted quadratic scaling and its coefficient by numerically solving the mode equation. These results identify the regularity of the scale factor in the sharp limit as the key property controlling the sharp-transition enhancement.

arXiv comment6 pages, 1 figure