Gravitational wave signatures of cogenesis from a burdened PBH

We explore the possibility of explaining the observed dark matter (DM) relic abundance, along with matter-antimatter asymmetry, entirely from the evaporation of primordial black holes (PBH) beyond the semi-classical approximation. We find that, depending on the timing of modification to the semi-classical approximation and the efficiency of the backreaction, it is possible to produce the correct DM abundance for PBHs with masses $\gtrsim\mathcal{O}(10^3)$ g, whereas producing the right amount of baryon asymmetry requires light PBHs with masses $\lesssim\mathcal{O}(10^3)$ g, satisfying bounds on the PBH mass from the Cosmic Microwave Background and Big Bang Nucleosynthesis. However, in a simplistic scenario, achieving both {\it simultaneously} is not feasible, typically because of the stringent Lyman-$\alpha$ constraint on warm dark matter mass. In addition to DM and baryon asymmetry, we also investigate the impact of memory burden on dark radiation, evaporated from PBH, constrained by the effective number of relativistic degrees of freedom $\Delta N_{\rm eff}$. Furthermore, we demonstrate how induced gravitational waves from PBH density fluctuations can provide a window to test the memory-burden effects, thereby placing constraints on either the DM mass scale or the scale of leptogenesis.