Speaker
Description
Evaporating primordial black holes heat the surrounding plasma via Hawking radiation, forming localized hotspots whose temperature may far exceed that of the cosmological background. Previous studies of hotspot formation and cooling have treated the subsequent energy transport in flat spacetime, thereby neglecting the expansion of the Universe. We formulate the diffusion equation governing the hotspot evolution in an expanding universe, and clarify the regime in which the formalism is valid. We find that hotspot formation is robust against cosmological expansion, and the critical distance scale where Hubble expansion overtakes diffusion coincides with the decoupling radius introduced in earlier work. However, the cooling stage is substantially modified: the plateau temperature decreases more steeply than in the flat-spacetime treatment, and this scaling cannot be obtained by simply redshifting the flat-spacetime solution because expansion also suppresses diffusive transport. As a consequence, all hotspots disappear within a finite time, as opposed to the flat-spacetime prediction of everlasting hotspots in part of the parameter space.