Primordial black holes and gravitational waves induced by exponential-tailed perturbations

Abstract

Primordial black holes (PBHs) whose masses are in ∼ [10 −15 M , 10 −11 M ] have been extensively studied as a candidate of whole dark matter (DM). One of the probes to test such a PBH-DM scenario is scalar-induced stochastic gravitational waves (GWs) accompanied with the enhanced primordial fluctuations to form the PBHs with frequency peaked in the mHz band being targeted by the LISA mission. In order to utilize the stochastic GWs for checking the PBH-DM scenario, it needs to exactly relate the PBH abundance and the amplitude of the GWs spectrum. Recently in Kitajima et al. [1], the impact of the non-Gaussianity of the enhanced primordial curvature perturbations on the PBH abundance has been investigated based on the peak theory, and they found that a specific non-Gaussian feature called the exponential tail significantly increases the PBH abundance compared with the Gaussian case. In this work, we investigate the spectrum of the induced stochastic GWs associated with PBH DM in the exponential-tail case. In order to take into account the non-Gaussianity properly, we employ the diagrammatic approach for the calculation of the spectrum. We find that the amplitude of the stochastic GW spectrum is slightly lower than the one for the Gaussian case, but it can still be detectable with the LISA sensitivity. We also find that the non-Gaussian contribution can appear on the high-frequency side through their complicated momentum configurations. Although this feature emerges under the LISA sensitivity, it might be possible to obtain information about the non-Gaussianity from GW observation with a deeper sensitivity such as the DECIGO mission.

Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity f NL and g NL considered

“…Regarding to local-type non-Gaussianity f NL , complete analysis presented in refs. [23][24][25][26] show that this spectrum can be substantially enhanced, potentially reaching up to two orders of magnitude larger than the Gaussian scenario, depending on the levels of f NL . Other works related with the effects of primordial non-Gaussianity (e.g., f NL and g NL ) on SIGWs have been shown in refs.…”

“…By adopting the Feynman-like diagrammatic technique, the four-point correlator of Gaussian curvature perturbations can be described by a single diagram [16,17]. However, in the case of non-Gaussianity with a parameter f NL , the derivation process becomes significantly more involved, requiring the evaluation of a total of seven diagrams to calculate the four-point correlator of linear curvature perturbations [23][24][25][26]. The first complete analysis of this calculation can be found in ref.…”

“…Furthermore, relevant works on the primordial non-Gaussian parameter g NL can be found in refs. [26,[31][32][33]38].…”

“…In this study, we employ the diagrammatic approach, which has been extensively utilized in the literature [23][24][25][26], to investigate the local-type primordial non-Gaussianity, parameterized by f NL and g NL , of curvature perturbations within the theoretical framework of SIGWs. This work serves as a natural extension of our previous research [25], which focused solely on f NL .…”

“…The diagrammatic technique has been widely used in quantum field theory and cosmology. Recently, it has been applied to calculate the energy-density fraction spectrum of SIGWs [23,24,26], as well as the angular power spectrum [25,106]. This technique has the potential to overcome the challenges encountered when expanding multi-point correlators using Wick's theorem.…”