[Paper Review] A topic review on probing primordial black hole dark matter with scalar induced gravitational waves

Chen Yuan, Qing-Guo Huang|arXiv (Cornell University)|Mar 8, 2021

Cosmology and Gravitation Theories4 citations

TL;DR

This review explores scalar-induced gravitational waves (SIGWs) as a probe for primordial black hole (PBH) dark matter, demonstrating that SIGWs generated during PBH formation provide stringent constraints on PBH mass fractions. It shows that LISA and pulsar timing arrays can detect SIGWs from monochromatic PBHs across key mass windows, with non-Gaussianities significantly altering signal amplitudes and complicating detection.

ABSTRACT

Primordial black holes (PBHs) are supposed to form from the collapse of over-densed regions generated by large scalar curvature perturbations in the radiation dominated era. Despite decades of various independent observations, the nature of dark matter (DM) remains highly puzzling. Recently, PBH DM have aroused interest since they provide an attracting explanation to the merger events of binary black holes discovered by LIGO/VIRGO and may play an important role on DM. During the formation of PBH, gravitational waves will be sourced by linear scalar perturbations at second-order, known as the scalar-induced gravitational waves (SIGWs), which provides a new way to hunt for PBH DM. This topic review mainly focus on the physics about SIGWs accompanying the formation of PBH DM.

Motivation & Objective

• To review the physics of scalar-induced gravitational waves (SIGWs) generated during the formation of primordial black holes (PBHs).
• To assess the potential of SIGWs as a probe for PBH dark matter, especially in light of LIGO/Virgo binary black hole merger observations.
• To examine the impact of primordial non-Gaussianities on SIGW amplitudes and detectability by current and future gravitational wave detectors.
• To evaluate the constraints on PBH dark matter fraction ($f_{\mathrm{pbh}}$) derived from SIGW signals, particularly using NANOGrav 11-year data.
• To identify open challenges, including the effects of the QCD phase transition and higher-order corrections on SIGW waveforms and detection prospects.

Proposed method

• Modeling PBH formation via second-order scalar perturbations in the radiation-dominated era, using the curvature perturbation and density contrast relation.
• Calculating SIGW energy density spectra using second-order perturbation theory in a cosmological background, including corrections up to third order.
• Incorporating primordial non-Gaussianities (local-type $F_{\mathrm{NL}}$, $G_{\mathrm{NL}}$) to assess their impact on SIGW amplitudes and detectability.
• Applying window functions and power spectra (log-normal, box, $\delta$-spectrum) to compute PBH mass functions and SIGW signals across different scales.
• Comparing theoretical SIGW predictions with sensitivity curves of LISA, IPTA, FAST, and SKA to estimate signal-to-noise ratios (SNR).
• Using null detection of SIGWs in NANOGrav 11-year data to derive upper bounds on $f_{\mathrm{pbh}}$, incorporating constraints from microlensing and binary PBHs.

Experimental results

Research questions

• RQ1 How do scalar-induced gravitational waves (SIGWs) arise during the formation of primordial black holes (PBHs) in the radiation-dominated era?
• RQ2 To what extent do primordial non-Gaussianities ($F_{\mathrm{NL}}$, $G_{\mathrm{NL}}$) suppress or alter the amplitude and shape of SIGW signals?
• RQ3 Can LISA and pulsar timing arrays (PTAs) detect SIGWs from monochromatic PBHs across the mass window $[10^{-16},10^{-14}] \cup [10^{-13},10^{-12}] M_\odot$?
• RQ4 How do the QCD phase transition and equation of state changes affect the SIGW waveform and detection prospects?
• RQ5 What are the most stringent current constraints on the PBH dark matter fraction ($f_{\mathrm{pbh}}$) derived from SIGW null detections?

Key findings

• SIGWs provide the most stringent constraints on $f_{\mathrm{pbh}}$ in certain mass ranges, surpassing other observational methods by several orders of magnitude.
• For monochromatic PBHs representing all dark matter in the $[10^{-16},10^{-14}] \cup [10^{-13},10^{-11}] M_\odot$ window, LISA and PTAs are expected to detect SIGW signals regardless of $F_{\mathrm{NL}}$-type non-Gaussianities.
• At $G_{\mathrm{NL}}$-order, non-Gaussianities suppress SIGW amplitudes further, potentially evading detection by LISA even if PBHs constitute all dark matter.
• The power spectrum and non-Gaussianity parameters are degenerate in SIGW signals, making independent measurements necessary to disentangle them.
• NANOGrav 11-year data null detection sets upper limits on $f_{\mathrm{pbh}}$ below $10^{-6}$ in the $10^{-13} \sim 10^{-12} M_\odot$ range, excluding significant PBH contributions.
• The inclusion of third-order corrections and QCD phase transition effects modifies the SIGW spectrum, particularly in the PTA frequency band, necessitating more realistic modeling for accurate detection forecasts.