[Paper Review] Cosmological Background Interpretation of Pulsar Timing Array Data

Daniel G. Figueroa, Mauro Pieroni+2 more|arXiv (Cornell University)|Jul 5, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy200 references11 citations

TL;DR

The paper analyzes NG15 and EPTA-DR2new PTA data to compare cosmological gravitational-wave background models against SMBHBs, finding scalar-induced and related signals often fit better, with strong constraints on primordial non-Gaussianity.

ABSTRACT

We discuss the interpretation of the detected signal by Pulsar Timing Array (PTA) observations as a gravitational wave background (GWB) of cosmological origin. We combine NANOGrav 15-years and EPTA-DR2new data sets and confront them against backgrounds from supermassive black hole binaries (SMBHBs), and cosmological signals from inflation, cosmic (super)strings, first-order phase transitions, Gaussian and non-Gaussian large scalar fluctuations, and audible axions. We find that scalar-induced, and to a lesser extent audible axion and cosmic superstring signals, provide a better fit than SMBHBs. These results depend, however, on modeling assumptions, so further data and analysis are needed to reach robust conclusions. Independently of the signal origin, the data strongly constrain the parameter space of cosmological signals, for example, setting an upper bound on primordial non-Gaussianity at PTA scales as $|f_{nl}| \lesssim 2.34$ at 95% CL.

Motivation & Objective

• Assess whether PTA-detected stochastic backgrounds favor cosmological or astrophysical (SMBHB) origins.
• Explore a wide range of cosmological GW background sources (inflation, strings, phase transitions, scalar fluctuations, audible axions).
• Derive constraints on model parameters and perform model selection to identify preferred scenarios.
• Quantify bounds on primordial non-Gaussianity and other early-Universe parameters from PTA data.

Proposed method

• Combine NG15 and EPTA-DR2new datasets in a Bayesian framework to fit multiple GWB templates.
• Parameterize spectra with power-law and broken-power-law forms, plus specific shapes for phase transitions, strings, and audible axions.
• Use independent-bin approximation for frequency points in the likelihood, with free spectra chains to obtain posteriors.
• Compute Bayes factors and Akaike Information Criterion to compare models against SMBHB baseline.
• Impose observational priors and external constraints (PBH, N_eff, lensing) where relevant to guide parameter inferences.

Experimental results

Research questions

• RQ1 Which GWB source classes provide the best fit to the combined PTA data relative to SMBHBs?
• RQ2 What are the posterior constraints on key cosmological parameters (e.g., fNL, Gμ for strings, axion parameters) from PTA observations?
• RQ3 Are there robust indications favoring scalar-induced GWB or related cosmological signals over astrophysical backgrounds?
• RQ4 How do model comparisons constrain inflationary, string, phase-transition, and atto-axion scenarios at PTA frequencies?

Key findings

• Gaussian and non-Gaussian scalar-induced GWB, and to a lesser extent audible axion and cosmic superstring signals, fit PTA data better than SMBHBs under certain modeling assumptions.
• PTA data constrain primordial non-Gaussianity to |fNL| ≲ 2.34 at 95% CL, a stringent bound at PTA scales.
• A Gaussian bump SIGWB (gSIGWB-bump) provides the strongest Bayes factors for both NANOGrav and EPTA, with BF_NANO = 120 and BF_EPTA = 15, and BF_comb ≈ 1300 for the combined data.
• SIGWB with local non-Gaussianity (ngSIGWB-bump) also fits well, BF_comb ≈ 780, and yields |fNL| ≲ 2.34 at 95% CL.
• Cosmic strings improve fit in some cases; field-theory strings are disfavored, while superstrings can fit data but imply a lower energy scale and depend on intercommutation probability (p).
• Audible axions impose lower bounds on m_a ≳ 8.0×10^-11 meV and f_a ≳ 1.3×10^18 GeV, with some tension from relic constraints.
• Combined data favor gSIGWB and ngSIGWB as strong performers, though overlapping pulsars limit definitive conclusions about the signal origin.
• The analysis yields valuable constraints on PBH abundance and other early-Universe parameters, highlighting PTA data's potential to probe high-energy cosmology.