Gravitational waves induced from primordial black hole fluctuations: the effect of an extended mass function

Abstract

The gravitational potential of initially Poisson distributed primordial black holes (PBH) can induce a stochastic gravitational-wave background (SGWB) at second order in cosmological perturbation theory. This SGWB was previously studied in the context of general relativity (GR) and modified gravity setups by assuming a monochromatic PBH mass function. Here we extend the previous analysis in the context of GR by studying the aforementioned SGWB within more physically realistic regimes where PBHs have different masses. In particular, starting from a power-law cosmologically motivated primordial curvature power spectrum with a running spectral index we extract the extended PBH mass function and the associated to it PBH gravitational potential which acts as the source of the scalar induced SGWB. At the end, by taking into account the dynamical evolution of the PBH gravitational potential during the transition from the matter era driven by PBHs to the radiation era we extract the respective GW signal today. Interestingly, in order to trigger an early PBH-dominated era and avoid the GW constraints at BBN we find that the running of the spectral index αs of our primordial curvature power spectrum should be within the narrow range αs ⋲ [3.316,3.355] × 10-3 while at the same time the GW signal is found to be potentially detectable by LISA.

Primordial Black Holes and Scotogenic dark matter

“…Finally, we comment that the amplitude of the induced GWs is extremely sensitive to the PBH mass spectrum [112,114,142]. The findings presented herein are contingent upon a monochromatic mass spectrum, and might be subject to modification if an extended mass function is considered.…”

Inflation and Primordial Black Holes

“…Along with a localized exponential amplification, the resulting power spectrum of curvature perturbation exhibits order-one oscillations in k, which is a common characteristic of sharp features [313,314], with a frequency set by the time of the turn. We will review these features below by focusing on the analytic model presented in [312] 37 . For this purpose, we consider an inflationary trajectory with a top-hat 38 sudden turn profile (see, e.g., the right panel in Figure 17) characterized by three parameters: N f , the central time of its location (measured with respect to the horizon exit time of the CMB pivot scale); its duration (δ) and typical (constant) value (η max ⊥ ) around N f :…”

“…See, e.g., the impact of extended mass functions on the PBH abundance constraints [27]. Ultralight PBHs with M pbh 10 15 g-although they cannot account for the DM density-may also have interesting observational effects if they come to dominate the energy budget of the universe before BBN (see, e.g., [36,37]).…”

“…Recall from our discussion above that entropic mass crossing at N f corresponds to the peak of the power spectrum. 37 For a detailed analytic/numerical analysis of the behavior of the power spectrum from strong sharp turns, see [72,73]. 38 More realistic models of the turn are expected to have a smooth time dependence of η ⊥ such as the Gaussian profile we considered earlier.…”

Gravitational wave hints black hole remnants as dark matter

“…Tiny PBHs have an interesting early Universe cosmology: they could totally (or partially) reheat the Universe [36][37][38][39] and explain the baryon asymmetry of the Universe [40][41][42][43][44][45][46][47][48][49][50][51][52]. Tiny PBHs also produce high frequency gravitational waves (GWs) by Hawking evaporation [45,[53][54][55][56][57][58][59][60][61], PBH binaries [54,57] and secondary GWs [57,[62][63][64][65][66][67][68]. See [57,65] for a recollection of GWs associated with tiny PBHs.…”