[Paper Review] The Detected Stochastic Gravitational Waves and Subsolar-Mass Primordial Black Holes

Keisuke Inomata, Kazunori Kohri+1 more|arXiv (Cornell University)|Jun 30, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy15 citations

TL;DR

The paper interprets the PTA-detected stochastic gravitational waves as scalar-induced GWs from primordial curvature perturbations and derives implications for subsolar-mass primordial black holes (PBHs). It finds that lighter PBHs around 10^-4 solar masses are favored by the data under a narrow (delta-function) curvature spectrum assumption.

ABSTRACT

Multiple pulsar timing array (PTA) collaborations recently announced the evidence of common-spectral processes caused by gravitational waves (GWs). These can be the stochastic GW background and its origin may be astrophysical and/or cosmological. We interpret it as the GWs induced by the primordial curvature perturbations and discuss their implications on primordial black holes (PBHs). We show that the newly released data suggest PBHs much lighter than the Sun ($\mathcal{O}(10^{-4}) \, M_\odot$ for the delta-function curvature spectrum; $< \mathcal{O}(10^{-2})\, M_\odot$ more generally) in contrast to what was expected from the previous PTA data releases.

Motivation & Objective

• Motivate how PTA-observed stochastic GWs can originate from cosmological sources beyond binary mergers.
• Show that scalar-induced GWs linked to enhanced curvature perturbations constrain PBH formation.
• Explore the mass and abundance range of PBHs implied by the GW data and existing constraints.
• Connect the GW signal shape to PBH mass scales and discuss observational prospects.

Proposed method

• Review the induced gravitational wave formalism in the Newtonian gauge with h_ij and scalar perturbations Phi.
• Adopt a delta-function (monochromatic) curvature power spectrum P_zeta = A_zeta delta(ln(k/k_*)) as a first step to interpret the SGWB.
• Compute the induced GW energy density during a radiation-dominated era using the kernel K(u,v) and the relation Omega_GW ~ integral over P_zeta(k) P_zeta(q).
• Relate the peak wavenumber k_* to PBH production scales and mass via M ~ 6.1e-4 M_sun (gamma=0.2, g_* factors).
• Use Carr/Press-Schechter formalism to estimate PBH abundance f_PBH from the threshold delta_c and variance sigma^2, with sigma^2 expressed through P_zeta and a transfer function T(q, k^-1).
• Map the degeneracy between A_zeta and f_PBH through the GW data to the M–f_PBH plane and compare with observational constraints.

Experimental results

Research questions

• RQ1 Can scalar-induced GWs from enhanced curvature perturbations explain the common-spectrum process seen by PTA collaborations?
• RQ2 What PBH mass range and abundance are implied if the SGWB is ascribed to scalar-induced GWs, and how do these compare to existing PBH constraints?
• RQ3 How does a delta-function curvature spectrum affect the predicted GW signal and PBH production?
• RQ4 To what extent do the OGLE microlensing events and HSC constraints align with the PBH interpretation of PTA data?
• RQ5 What future GW observations can test the PBH interpretation suggested by the PTA results?

Key findings

• The PTA data favor subsolar-mass PBHs, roughly in the range 5×10^-5 to 2×10^-3 solar masses, under the delta-function curvature spectrum assumption.
• The induced GW spectrum in the IR tail scales as f^2, with a degeneracy between A_zeta and f_* that extends the viable parameter space to higher frequencies than the nanohertz band.
• There is a shaded region excluded by dark radiation constraints from BBN, limiting the allowable GW energy density.
• A scenario with PBHs of mass around 6×10^-5 M_sun and f_PBH ≈ 2×10^-2 can partially explain OGLE microlensing events when combined with OGLE+HSC data.
• Merger-based SGWB spectra from these light PBHs can be tested by future GW detectors, though the peaks shift to higher frequencies compared to heavier PBH scenarios.
• The conclusions depend on uncertainties in window functions and the threshold delta_c, and may change with non-Gaussianity considerations not included in this work.