Anomaly-Sensitive Non-Gaussian Spectroscopy of the Stochastic GW Background across nHz–mHz–μHz

Inui et al. (2024) show that logarithmic non-Gaussianity in the primordial curvature perturbations can yield detectable scalar-induced gravitational waves (SIGWs) and produce parameter-dependent anomalies (e.g., PBH overproduction tension). Standard stochastic searches, however, assume a Gaussian, isotropic background. This project introduces a “non-Gaussian spectroscopy” pipeline that explicitly fits for higher-order statistics (bispectrum, trispectrum) and scale-dependent skewness/kurtosis in cross-correlated data from LISA-like interferometers and PTA-style datasets, augmented by FRB-timing baselines that probe the μHz gap (Lu, Wang, Xiao 2024). The core novelty is twofold: (i) we treat non-Gaussianity as signal, not nuisance, constructing optimal estimators for non-Gaussian features predicted by logarithmic non-Gaussianity; and (ii) we jointly analyze multiple bands—nHz (PTAs), μHz (FRBs), mHz (LISA)—to hunt for consistent non-Gaussian patterns across frequencies. Practically, we would inject non-Gaussian SIGW realizations into simulated global-fit analyses (Strub et al. 2023; Weaving et al. 2023) to quantify detectability and degeneracies with astrophysical confusion backgrounds. This directly tests Inui et al.’s parameter space and may alleviate the PBH-overproduction tension by targeting regimes where the background is detectably non-Gaussian even when the mean spectrum is ambiguous. If successful, it upgrades stochastic background searches from “power-spectrum-only” to “distribution-aware” inference, opening a new axis of discovery for early-Universe physics.

References:

1. Primordial black holes and induced gravitational waves from logarithmic non-Gaussianity. Ryoto Inui, Cristian Joana, Hayato Motohashi, Shi Pi, Yuichiro Tada, Shuichiro Yokoyama (2024). Journal of Cosmology and Astroparticle Physics.
2. A New Probe of $\mu$Hz Gravitational Waves with FRB Timing. Zhiyao Lu, Lian-Tao Wang, Huangyu Xiao (2024).
3. Adapting the PyCBC pipeline to find and infer the properties of gravitational waves from massive black hole binaries in LISA. C. Weaving, L. Nuttall, I. Harry, Shichao Wu, A. Nitz (2023). Classical and quantum gravity.
4. Accelerating global parameter estimation of gravitational waves from Galactic binaries using a genetic algorithm and GPUs. Stefan H. Strub, L. Ferraioli, C. Schmelzbach, S. Stähler, D. Giardini (2023). Physical Review D.