Constraining regular primordial black holes with isocurvature gravitational waves

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 $\Delta N_{\rm eff}$, 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.