Discriminating Between Models of the Nanohertz Gravitational-Wave Background with Pulsar Timing Arrays

Abstract: Recent pulsar timing array results, including the NANOGrav 15-year data set, show evidence for a stochastic gravitational-wave background (GWB) in the nanohertz band. We present a Bayesian framework to compare three possible origins: (i) a background from supermassive black hole binary mergers, (ii) a first-order phase transition in the early Universe, and (iii) a network of cosmic strings. We derive the PTA likelihood with the Hellings-Downs angular correlation and model intrinsic pulsar red noise and dispersion-measure variations. Using Bayesian model selection, we infer posteriors for the GWB amplitude and spectral slope and compute marginal likelihoods for each scenario. We confirm a common-spectrum process with Hellings-Downs spatial correlations and recover a characteristic strain amplitude at f_yr = 1/year of A_GWB approx 2.4e-15, with a slope consistent with gamma approx 13/3 as expected for supermassive black hole binaries. While fully consistent with an astrophysical origin, cosmological sources are not excluded: cosmic strings with Gmu ~ 1e-11 to 1e-10 and phase transitions peaking near 1e-8 to 1e-7 Hz can reproduce the observed amplitude within allowed parameter ranges. Current Bayes factors do not show a decisive preference among these scenarios. We discuss noise-mitigation implications and prospects for discrimination with future PTA observations.