Gravitational Dark Matter from Curved Spacetime: Cosmological Particle Production in Open and Closed Universes

Despite decades of searches, no evidence for weakly interacting massive particles (WIMPs) has been found, leaving the nature of dark matter an open question. This motivates exploring alternative production mechanisms for dark matter arising purely from gravity. Cosmological gravitational particle production (CGPP) offers such a mechanism, converting the rapid change of spacetime at the end of inflation into real particles. I study how spatial curvature alters CGPP for scalar fields by solving the mode equations in closed (positive curvature) and open (negative curvature) Friedmann–Robertson–Walker (FRW) backgrounds and by computing the resulting spectra and relic yields (dark matter and total energy density). In positive curvature, curvature has little impact—results closely track the flat space approximation. In negative curvature, curvature induces controlled corrections and can add large-scale contributions through possible "supercurvature" modes (modes with wavelength larger than the curvature radius). I present parameter-space scans over mass, expansion history, and curvature scale for both signs of curvature, delineating where curvature effects are negligible and where they must be included. By identifying when curvature significantly modifies gravitational particle production, this work refines predictions for purely gravitational dark matter and clarifies the conditions under which it can account for the observed cosmic abundance.