Primordial Black Holes: A Window into Dark Matter and Gravitational Wave Sources

Primordial black holes (PBHs) provide a unique probe of the 
poorly understood epoch between inflation and Big-Bang nucleosynthesis, 
where direct observational access remains limited. In this talk, I will 
discuss how PBHs connect early-Universe cosmology, dark matter, and 
gravitational-wave (GW) phenomenology. After briefly motivating PBHs as 
probes of reheating, I will focus on stochastic GW backgrounds in 
PBH-related scenarios across a wide range of frequencies, from nano-Hz 
scales relevant for pulsar timing arrays such as NANOGrav to milli-Hz 
and Hz–kHz bands probed by future detectors such as LISA and the 
Einstein Telescope. I will discuss both primary tensor modes and 
scalar-induced secondary GWs generated during reheating, emphasising 
how their spectra encode information about the thermal history of the 
Universe and possible non-standard expansion phases. I will also 
discuss other induced GW signals relevant to PBH reheating, 
particularly those sourced by PBH number-density fluctuations, which 
generate an isocurvature component alongside the standard adiabatic 
perturbations. I will comment on how these signals are modified by 
non-standard cosmological phases or by quantum-corrected Hawking 
evaporation, and on whether these effects can give rise to a degeneracy 
between the non-standard expansion history and the memory-burden 
parameter. Finally, I will discuss how dark matter production from 
evaporating PBHs can modify the allowed dark matter parameter space in 
the PBH reheating context, with implications for both WIMP and FIMP 
scenarios, and briefly comment on how PBH-induced GW signals may also 
play a role in precision measurements of the Hubble parameter.
(Based on Phys. Rev. D 104, 063513 (2021); JCAP 01 (2025) 118; JHEP 10 
(2024) 142; arXiv:2603.25795; JCAP 07 (2024) 002; arXiv:2602.15026; and 
arXiv:2604.22731.)