Inflationary primordial black holes for the LIGO gravitational wave events and pulsar timing array experiments

TL;DR

The paper investigates whether LIGO-detected black hole mergers could originate from primordial black holes formed by inflationary fluctuations. It emphasizes that second-order gravitational waves and CMB μ-distortion markedly constrain the required small-scale curvature perturbations, favoring a very sharply peaked spectrum at high wavenumbers and challenging simple Gaussian single-field models. A double-inflation framework is proposed to realize such a sharp peak, with the authors showing concrete parameter regimes that can yield PBHs in the LIGO mass range while avoiding current PTA and μ bounds; however, these scenarios remain testable by future experiments like SKA and space-based CMB missions. The study highlights the interplay between PBH formation, induced GWs, and observational probes, offering pathways to confirm or exclude inflationary PBHs as LIGO sources.

Abstract

Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early Universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GW events as mergers of PBHs which are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs and thus we have several other probes to test this scenario. We point out that the current pulsar timing array (PTA) experiments already put severe constraints on GWs generated via the second-order effects, and that the observation of the cosmic microwave background (CMB) puts severe restriction on its $μ$ distortion. In particular, it is found that the scalar power spectrum should have a very sharp peak at $k \sim 10^{6}$ Mpc$^{-1}$ to fulfill the required abundance of PBHs while evading constraints from the PTA experiments together with the $μ$ distortion. We propose a mechanism which can realize such a sharp peak. In the future, simple inflation models that generate PBHs via almost Gaussian fluctuations could be probed/excluded.

Figures (5)

• Figure 1: Black dashed line: the PBH mass spectra for parameters given in Eq. \ref{['eq:not_cancel']} ($c_\text{kin}>0$). Cyan solid line: that for parameters given in Eq. \ref{['eq:cancel']} ($c_\text{kin} < 0$). Observationally excluded regions which do not depend on the production mechanism of PBHs are represented by gray-shaded regions: extragalactic gamma rays from Hawking radiation Carr:2009jm, femtolensing of known gamma ray bursts Barnacka:2012bm, white dwarfs existing in our local galaxy Graham:2015apa, Kepler micro/millilensing Griest:2013esa, EROS/MACHO microlensing Tisserand:2006zx, and accretion constraints from CMB Ricotti:2007au. See also Carr:2016drx for a recent summary of observational constraints on PBHs. We then show the constraints on inflationary PBHs in the orange and green shaded regions: the secondary GW constraint with use of the EPTA experiment Lentati:2015qwp and the current $\mu$ distortion constraint $|\mu|<9\times10^{-5}$ by green- and orange-shaded regions for a monochromatic mass spectrum. Note that the exact constraints depend on the shape of the power spectrum and therefore the illustrated green/orange constraints are just rough indicators. (See also discussion on uncertainties at the end of Sec. \ref{['sec:pbhligo']}.) We have provided two sample parameter sets of the double inflation model as an example, which will be discussed in Sec. \ref{['sec:double_inf']}. Both black dashed [Eq. \ref{['eq:not_cancel']}] and cyan solid [Eq. \ref{['eq:cancel']}] PBH mass spectra seem to avoid these constraints in this figure, but the black dashed one is actually disfavored by PTA constraints as shown in Fig. \ref{['fig:GW']}.
• Figure 2: Black dashed line: the induced GW spectra for parameters given in Eq. \ref{['eq:not_cancel']} ($c_\text{kin}>0$). Cyan solid line: that for parameters given in Eq. \ref{['eq:cancel']} ($c_\text{kin} < 0$). We also plot $\Omega_\text{GW} (k) = \Omega_\text{GW, peak} (k_i/k)^4$ in a black dotted line for comparison. The current three severe constraints, i.e., NANOGrav Arzoumanian:2015liz, EPTA Lentati:2015qwp, and PPTA Shannon:2015ect are shown in green-shaded regions. The prospect of the SKA sensitivity is shown in a green dotted line Moore:2014lgaJanssen:2014dka. Although the case of $c_\text{kin} > 0$ is marginal, we cannot immediately exclude it because of the uncertainty of the factor $\gamma$. A slightly small $\gamma$ is enough to elude this constraint.
• Figure 3: Black dashed line: the scalar power spectra for parameters given in Eq. \ref{['eq:not_cancel']} ($c_\text{kin}>0$). Cyan solid line: that for parameters given in Eq. \ref{['eq:cancel']} ($c_\text{kin} < 0$). Here we show the constraints from the $\mu$ distortion with the current constraint $|\mu|<9\times10^{-5}$Fixsen:1996nj by an orange-shaded region and the future prospect $|\mu|<10^{-9}$Kogut:2011xwAndre:2013afa by a orange dotted line.
• Figure 4: The excluded parameter regions by the current PTA constraints (large green dots), the current $\mu$ constraint $|\mu|<9\times10^{-5}$ (large orange dots), and the future prospect $|\mu|<10^{-9}$ (small orange dots) with the assumption that the PBH mass spectrum becomes maximal as $\Omega_\text{PBH}/\Omega_c=10^{-4}$ at $30M_\odot$. The future SKA experiment would exclude all regions though we do not plot them to avoid a busy figure.
• Figure 5: The schematic image of the multiple horizon crossing mode $k$. $a_\text{pre,f}$ and $a_\text{new,i}$ represent the time of the end of the pre-inflation and the beginning of the second new inflation.