Constraining regular primordial black holes with isocurvature gravitational waves

TL;DR

The paper addresses how ultra-light regular primordial black holes (RPBHs) can be constrained by isocurvature gravitational waves (GWs) generated if they temporarily dominate the early Universe and subsequently evaporate. It develops a generic framework linking Poisson fluctuations in an RPBH population to an isocurvature GW spectrum, propagates the signal through cosmic history, and constrains the total GW energy using the bound on $\Delta N_{\rm eff}$. The Simpson-Visser metric is used as an explicit demonstration, showing that longer-lived RPBHs produce stronger GW backgrounds and tighter population bounds relative to Schwarzschild PBHs. The results indicate that the allowed PBH fraction $\beta$ is reduced for longer-lived RPBHs, and the peak GW frequency shifts to lower values, highlighting the sensitivity of cosmological GWs to black hole interior physics. The approach offers a new probe of regular interiors and evaporation dynamics, with potential extensions to other regular metrics, extended mass functions, and spinning RPBHs.

Abstract

We find the constraint on the population of ultra-light regular primordial black holes (RPBHs) by using isocurvature gravitational waves (GW). If ultra-light RPBHs dominated the early Universe, the initial isocurvature perturbation is converted into curvature perturbation that induce second-order GW background upon evaporation of RPBHs. The upper limit of extra relativistic degrees of freedom $ΔN_{\rm eff}$, which could be inferred from Big Bang Nucleosynthesis or Cosmic Microwave Background observations, places a constraint on the maximum energy density of GW, which in turn can be used to constrain the RPBH population. As RPBHs have different lifetime from their singular counterparts, the constraint must be modified accordingly. While the formalism that we provide is generic, we work out explicitly the case of Simpson-Visser metric for demonstration. The RPBHs associated with this metric have lower Hawking temperature and smaller horizon size, leading to a longer lifetime than the singular Schwarzschild black holes. This implies a stronger constraint on RPBH population as they dominate the Universe for a longer period of time and generate stronger GW.

Figures (3)

• Figure 1: Isocurvature GW spectrum of Schwarzschild PBH and Simpson-Visser RPBH. The dashed black line indicates the upper bound on $\Omega_\text{GW,0}^\text{tot}$ coming from $\Delta N_\text{eff}$ constraint. The solid black contours are power-law integrated sensitivity curves of BBO and ET taken from Schmitz:2020syl.
• Figure 2: Allowed parameter space for the Schwarzschild PBH (shaded blue) and the Simpson-Visser RPBH (shaded green) where we can have isocurvature GW that is still consistent with $\Delta N_\text{eff}$ constraint. The parameter space below the $\beta_c$ line is not ruled out; it is just where we don't have PBH domination and thus isocurvature GW. However, the parameter space above the $\beta_\text{max}$ line is absolutely ruled out as there will be PBH domination with too strong isocurvature GW that is not permitted by $\Delta N_\text{eff}$ constraint.
• Figure 3: Constraints on the population PBH as a function of regularizing parameter $l$.