[Paper Review] Limits on scalar-induced gravitational waves from the stochastic background by pulsar timing array observations

Yi-Fu Cai, Xin-Chen He+3 more|PubMed|Jun 30, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy101 references7 citations

TL;DR

The paper constrains the energy spectrum of scalar-induced gravitational waves (IGWs) using NANOGrav, PPTA, and EPTA data by fitting a smooth broken power-law model to the SGWB, and discusses implications for primordial black holes and inflation models.

ABSTRACT

Recently, the NANOGrav, PPTA, EPTA, and CPTA Collaborations independently reported their evidence of the Stochastic Gravitational Waves Background (SGWB). While the inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from the population of supermassive black-hole binaries (SMBHBs), the search for new physics remains plausible in this observational window. In this work, we explore the possibility of explaining such a signal by the scalar-induced gravitational waves (IGWs) in the very early universe. We use a parameterized broken power-law function as a general description of the energy spectrum of the SGWB and fit it to the new results of NANOGrav, PPTA and EPTA. We find that this approach can put constraints on the parameters of IGW energy spectrum and further yield restrictions on various inflation models that may produce primordial black holes (PBHs) in the early universe, which is also expected to be examined by the forthcoming space-based GW experiments.

Motivation & Objective

• Motivate the search for SGWB sources beyond SMBHBs in the PTA band and explore IGWs as a cosmological origin.
• Parameterize the IGW energy spectrum with a smooth broken power-law and constrain its shape using PTA datasets.
• Infer implications for early-universe models that generate enhanced small-scale scalar perturbations and PBHs.
• Assess potential future tests with space-based GW observatories for the UV tail of the IGW spectrum.

Proposed method

• Adopt a smooth broken power-law parameterization of the IGW energy spectrum, Omega_GW(f) h_0^2 = A (alpha+beta)/[beta (f/f_c)^(-alpha) + alpha (f/f_c)^beta].
• Use Bayesian inference with MCMC (emcee) to fit the spectrum to NANOGrav, PPTA, and EPTA results.
• Compute likelihood as a product of frequency-bin kernels L_i(Omega_GW(f_i; Theta)).
• Infer posterior distributions for parameters (log A, log f_c, alpha, beta) with uniform priors on alpha, beta and log-uniform priors on A and f_c.
• Compare inferred IGW spectra to PTA observations and discuss IR/UV behavior and potential space-based GW tests.
• Discuss how the IR tail (f << f_c) and UV tail (f > f_c) influence interpretation and future observations.

Experimental results

Research questions

• RQ1 Can scalar-induced gravitational waves with a broken power-law spectrum explain the SGWB hinted by PTA collaborations beyond SMBHBs?
• RQ2 What ranges for the IGW energy-spectrum parameters (A, f_c, alpha, beta) are favored by NANOGrav, PPTA, and EPTA data?
• RQ3 What do the inferred spectrum shapes imply about small-scale primordial perturbations and related PBH formation scenarios?
• RQ4 To what extent can future space-based GW missions test the UV tail of the IGW spectrum and discriminate among models?

Key findings

• PTA datasets favor a blue-tilted IR region in the IGW spectrum with alpha values around 0.8–1.3 (varies by dataset).
• Best-fit peak frequency f_c is constrained to be greater than roughly 10^-7 Hz at 2-sigma for the IGW interpretation.
• Maximum Omega_GW h_0^2 is suggested to exceed 10^-8 with f_c > 10^-8 Hz, depending on dataset.
• The UV tail is relatively gentle for smaller beta, potentially detectable by future space-based GW observatories (LISA/TianQin/Taiji).
• The results imply quasi-monochromatic PBH masses smaller than about 0.1 M_sun in the IGW/PBH connection, depending on non-Gaussianity assumptions.