A Search for a Thermal Spectral Bump in the Nanohertz Stochastic Gravitational-Wave Background with NANOGrav

Pulsar timing array (PTA) collaborations have established strong evidence for a stochastic gravitational-wave background (SGWB) in the nanohertz band, generally attributed to an incoherent superposition of supermassive black-hole binary (SMBHB) inspirals with a characteristic $\Omega_{CW}(f)\propto f^{2/3}$ spectrum. A separate and growing literature considers non-power-law "bump" features in the SGWB, motivated by first-order phase transitions, preheating, or other resonant phenomena in the early Universe [2, 3]. Motivated by a phenomenological model in which primordial modes exiting the horizon ~35-41 e-folds before the end of inflation are predicted, under standard single-field slow-roll inflation, to redshift into the nanohertz band today, we search for a log-Gaussian thermal-like bump superimposed on the standard astrophysical background using the NANOGrav 15-year data set. We construct a Bayesian pipeline (NUTS/NumPyro with a Hellings-Downs spatial covariance) applied to 76 pulsars, and validate it by recovering $log_{10}A_{GW}=-14.53_{-1.26}^{+1.41}$ and consistent with the published NANOGrav result. We find no evidence for the proposed bump: the posterior on the bump amplitude $log_{10}\Omega_{fork}$ is essentially unconstrained by the data across a wide prior, and the log Bayes factor between the bump and no-bump models is consistent with zero ($ln~BF\approx0$). We report the corresponding upper limit and discuss the methodological lessons for constructing falsifiable spectral-bump searches in PTA data