Spontaneous Baryogenesis and Primordial Black Hole Dark Matter from Ultra-Slow-Roll Inflation

We propose a unified framework where the totality of dark matter (DM), the baryon asymmetry of the universe, and a detectable stochastic gravitational wave (GW) background originate from ultra-slow-roll (USR) inflation. The drastic suppression of the inflaton velocity during the USR phase, required for primordial black hole (PBH) DM production, can also set the initial conditions for spontaneous baryogenesis via a derivative coupling. This mechanism establishes a predictive correlation between the PBH abundance and the baryon yield, effectively fixing the reheating temperature $T_\textrm{reh}$ as a function of the post-peak spectral slope of the primordial power spectrum and the tensor-to-scalar ratio on CMB scales $r_\textrm{CMB}$. We perform a simple scan of the parameter space, demonstrating that while ``flat'' spectral tails allow for high-scale inflation ($r_{\rm CMB} \lesssim 10^{-3}$, $T_{\rm reh} \lesssim 10^{14} \text{ GeV}$) with a small wedge of tensor-to-scalar ratios potentially accessible to future CMB B-mode experiments, steep spectral tails enforce drastically lower scale inflation with an unobservably small $r_{\rm CMB}$ to avoid baryon overproduction. This degeneracy can be broken by GW astronomy: while LISA and DECIGO are capable of detecting the induced GW background associated with asteroid-mass PBH DM, the Einstein Telescope (ET) can act as a spectral discriminator, sensitive only to the broadband signals of high-scale scenarios.