[Paper Review] Search for scalar induced gravitational waves in the International Pulsar Timing Array Data Release 2 and NANOgrav 12.5 years datasets

Virgile Dandoy, Valerie Domcke+1 more|arXiv (Cornell University)|Feb 15, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy104 references9 citations

TL;DR

The authors perform a Bayesian search for scalar-induced gravitational waves in IPTA DR2 and NG12 datasets, finding IPTA DR2 favors an astrophysical background while NG12 fits both scalar-induced and SMBHB backgrounds; they derive upper limits on the curvature power spectrum at small scales.

ABSTRACT

We perform a Bayesian search in the latest Pulsar Timing Array (PTA) datasets for a stochastic gravitational wave (GW) background sourced by curvature perturbations at scales $10^5~ ext{Mpc}^{-1}\lesssim k\lesssim 10^8~ ext{Mpc}^{-1}$. These re-enter the Hubble horizon at temperatures around and below the QCD crossover phase transition in the early Universe. We include a stochastic background of astrophysical origin in our search and properly account for constraints on the curvature power spectrum from the overproduction of primordial black holes (PBHs). We find that the International PTA Data Release 2 significantly favors the astrophysical model for its reported common-spectrum process, over the curvature-induced background. On the other hand, the two interpretations fit the NANOgrav 12.5 years dataset equally well. We then set new upper limits on the amplitude of the curvature power spectrum at small scales. These are independent from, and competitive with, indirect astrophysical bounds from the abundance of PBH dark matter. Upcoming PTA data releases will provide the strongest probe of the curvature power spectrum around the QCD epoch.

Motivation & Objective

• Motivate and search for a stochastic GW background sourced by curvature perturbations at small scales (k ~ 10^5–10^8 Mpc^-1) using PTA datasets.
• Incorporate an astrophysical SMBHB background and PBH-based constraints to assess the viability of a curvature-induced GW signal.
• Utilize a log-normal curvature power spectrum to study broad and narrow peaks and derive PBH-based upper bounds on P_zeta.
• Quantify how cosmological constraints, especially PBH overproduction and QCD-era dynamics, impact the scalar-induced GW interpretation.

Proposed method

• Adopt a Bayesian framework with the scalar-induced GW spectrum model Omega_gw h^2 ~ 1.9×10^-9 (A_zeta/0.01)^2 ... S(f/f_*) (App. A) and a log-normal P_zeta(k) with peak at k_* and width Delta.
• Parameterize the GW signal by A_zeta, k_*, Delta, and include an SMBHB background with amplitude A_SMBHBs.
• Impose PBH overproduction constraints to bound A_zeta, exploring Delta=1 (broad) and Delta=0.05 (narrow) cases.
• Use the IPTA DR2 and NG12 timing-residual cross-power spectral density with the Overlap Reduction Function and auto-correlation terms.
• Account for g_* and g_*s(T_*) dependence, and apply priors and nuisance noise modeling consistent with NG12 and IPTA DR2 analyses (App. C).
• Approximate scalar-induced GW spectra in IR tail for Delta ≤ 0.5 using improved analytical approximations (App. A).

Experimental results

Research questions

• RQ1 Can a scalar-induced GW background from small-scale curvature perturbations explain the PTA common-spectrum signal in IPTA DR2 and NG12?
• RQ2 How do PBH overproduction constraints limit the allowed curvature power spectrum amplitude A_zeta at PTA scales?
• RQ3 What is the relative likelihood of scalar-induced GWs versus an SMBHB background in IPTA DR2 and NG12 datasets when both are included?
• RQ4 What upper limits on the curvature power spectrum amplitude A_zeta arise when an SMBHB background is present?
• RQ5 How do peak width Delta and peak location k_* affect the interpretation and constraints of the PTA data?

Key findings

• IPTA DR2 data favor an astrophysical SMBHB background over a curvature-induced GW background for the common-spectrum process.
• NG12 data yield comparable fits to both scalar-induced and SMBHB backgrounds, allowing either interpretation.
• PBH overproduction constraints impose upper bounds on A_zeta that are strong and depend on Delta, with A_zeta ≲ ~0.01–0.04 for Delta=1 or 0.05 under certain assumptions.
• Maximum-likelihood scalar-induced GW spectra are obtained with k_* ~ few×10^6 Mpc^-1 and Delta ~ O(1), but PBH bounds restrict the allowed region.
• When including an SMBHB background, the study derives 95% CL upper limits on the curvature power spectrum amplitude A_zeta that are independent from PBH-based indirect bounds.
• The results indicate upcoming PTA data releases will be the strongest probe of the curvature power spectrum around the QCD epoch.