Stochastic gravitational waves associated with the formation of primordial black holes

TL;DR

This work analyzes stochastic gravitational waves produced during primordial black hole (PBH) formation, focusing on how induced GWs at second order in scalar perturbations depend on the (non-)Gaussian nature of the primordial fluctuations. It clarifies the mass-frequency relation that ties PBH mass to the typical GW frequency, showing that PBHs around tens of solar masses correspond to nanohertz GWs detectable by pulsar timing arrays. The authors demonstrate that Gaussian perturbations push the induced GW signal toward PTA limits, potentially ruling out such PBH scenarios unless non-Gaussianity suppresses the signal; conversely, certain non-Gaussian models (including $f_{\mathrm{NL}}$, $g_{\mathrm{NL}}$-type local non-Gaussianity and generalized tail PDFs) can evade these constraints or even enhance the signal, depending on the parameters. They conclude that current and future PTA and SKA observations can jointly constrain PBH abundance and small-scale non-Gaussianity, while noting that some inflationary scenarios can yield PBHs with suppressed induced GWs and still serve as DM candidates.

Abstract

Primordial black hole (PBH) mergers have been proposed as an explanation for the gravitational wave events detected by the LIGO collaboration. Such PBHs may be formed in the early Universe as a result of the collapse of extremely rare high-sigma peaks of primordial fluctuations on small scales, as long as the amplitude of primordial perturbations on small scales is enhanced significantly relative to the amplitude of perturbations observed on large scales. One consequence of these small-scale perturbations is generation of stochastic gravitational waves that arise at second order in scalar perturbations, mostly before the formation of the PBHs. These induced gravitational waves have been shown, assuming gaussian initial conditions, to be comparable to the current limits from the European Pulsar Timing Array, severely restricting this scenario. We show, however, that models with enhanced fluctuation amplitudes typically involve non-gaussian initial conditions. With such initial conditions, the current limits from pulsar timing can be evaded. The amplitude of the induced gravitational-wave background can be larger or smaller than the stochastic gravitational-wave background from supermassive black hole binaries.

Figures (3)

• Figure 1: Top: The ratio $\zeta_{\mathrm{th}}/\sigma$ as a function of $p$, controlling deviation from a gaussian PDF in Eq. (\ref{['pdf2']}), with $\beta=10^{-8}$. When $p=2$ the PDF is gaussian, for which $\zeta_{\mathrm{th}}/\sigma\simeq 6$. Center: Dependence of global or induced GWs on $p$. Local gravitational waves due to non-spherical collapse are also shown, which do not depend on non-gaussianity (but see the footnote 7). Current limits from European Pulsar Timing Array Lentati:2015qwp (PTA), a prediction of stochastic gravitational waves from supermassive black hole (SMBH) binaries and a predicted sensitivity of the Square Kilometer Array (SKA) Kramer:2010tm are also shown. Bottom: The dependence of induced GWs on $\beta$.
• Figure 2: Top: The dependence of the ratio $\zeta_{\mathrm{th}}/\sigma$ on $f_{\mathrm{NL}}$ of Eq. (\ref{['fnl']}). Bottom: The dependence of induced GWs on $f_{\mathrm{NL}}$.
• Figure 3: Top: The dependence of the ratio $\zeta_{\mathrm{th}}/\sigma$ on $g_{\mathrm{NL}}$ of Eq. (\ref{['gnl']}). Bottom: The dependence of induced GWs on $g_{\mathrm{NL}}$.