Can we distinguish the adiabatic fluctuations and isocurvature fluctuations with pulsar timing arrays?

Abstract

Understanding the nature of primordial fluctuations is pivotal to unraveling the Universe's early evolution. While these fluctuations are observed to be nearly scale-invariant, quasi-adiabatic, and Gaussian on large scales, their small-scale behavior remains poorly constrained, offering a potential window into new physics. Recent detections of a stochastic gravitational wave background in the nanohertz frequency range by pulsar timing arrays (PTAs), including NANOGrav, PPTA, EPTA+InPTA, and CPTA, align with astrophysical predictions from supermassive black hole binaries but could also encode signatures of primordial phenomena. We investigate whether the observed signal originates from primordial isocurvature or adiabatic fluctuations by fitting them to the latest NANOGrav dataset. Through comprehensive Bayesian model comparison, we evaluate the distinguishability of these scenarios given current PTA sensitivities. Our results demonstrate that existing data cannot conclusively differentiate between isocurvature and adiabatic sources, highlighting the need for enhanced observational capabilities to probe the primordial universe at small scales.