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

Abstract

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.

Figures (3)

• Figure 1: The peak amplitude $A_\textrm{PBH}$ as a function of PBH mass required for PBHs to saturate the DM density, i.e., $f_\textrm{PBH}=1$ assuming a narrow mass function for various inflationary spectral decay indices after the ultra-slow-roll phase.
• Figure 2: The parameter space for spontaneous baryogenesis compatible with $100\%$ PBH DM. The contours indicate the required reheating temperature $T_{\rm reh}$ versus the tensor-to-scalar ratio $r_\textrm{CMB}$ for different effective coupling scales $M_*$ of $M_{\rm Pl}$ (blue), $10^{16}$ GeV (purple) and $10^{14}$ GeV (cyan). The lower part of the blue region corresponds to $\alpha=0.25$ while the upper part corresponds to $\alpha=1$. The grey shaded regions represent physical exclusion zones: the upper region violates energy conservation ($T_{\rm reh} > V^{1/4}$), and the lower region violates the geometric duration of inflation ($k_{\rm end} < k_{\rm USR}$). Vertical lines indicate the current exclusion limit from BICEP/Keck ($r_\textrm{CMB} < 0.036$) and the projected sensitivity of future experiments like CMB-S4 ($r_\textrm{CMB} < 2\times 10^{-3}$) and PICO ($r_{\rm CMB}< 5\times 10^{-4}$). Top Row: Results for the standard slow-roll attractor tail ($n_{\rm exit} \approx -0.04$). Bottom Row: Results for steeper post-peak decays ($n_{\rm exit} = -1, -4$), which force the solution into a low-scale inflation regime with extremely suppressed $r_{\rm CMB}$.
• Figure 3: The predicted SNRs for LISA (blue), ET (purple), and DECIGO (cyan) as a function of the PBH mass $M_{\rm PBH}$ for 100% PBH DM. The different line styles correspond to different post-peak spectral slopes: flat-tail ($n_{\rm exit} =n_s-1$, solid), intermediate decay ($n_{\rm exit} = -1$, dashed), and steep decay ($n_{\rm exit} = -4$, dotted).