Disentangling the Origins of the NANOGrav Signal: Early Universe Models and $\Delta N_{eff}$ Bounds

TL;DR

This paper assesses whether early universe gravitational wave models can explain the NANOGrav signal without conflicting with CMB constraints on extra radiation, finding that some models could be detectable by future CMB experiments.

Contribution

It evaluates the compatibility of early universe gravitational wave models with current and future CMB bounds on $ _{eff}$, providing projections for detectability.

Findings

Models with $ _{eff}$ above CMB limits are excluded.

Current NANOGrav data has negligible impact on $ _{eff}$.

Future PTA observations could detect $ _{eff}$ signatures from inflation, SIGW, and cosmic strings.

Abstract

We investigate whether an Early-Universe stochastic gravitational-wave background (SGWB) can account for the common spectrum process reported by NANOGrav, while also being consistent with current and projected CMB measurements of extra radiation. We compute the contribution of effective number of relativistic species, $\Delta N_{eff}$, for a number of Early-Universe models proposed to explain the pulsar timing array (PTA) spectrum. We demonstrate that models predicting $\Delta N_{eff}$ above the CMB limit would be firmly excluded, implying that the NANOGrav signal in tension with these bounds must instead arise from astrophysical sources. We find that current NANOGrav 15-year dataset, sensitive up to 60 nHz, gives a negligible contribution to $\Delta N_{eff}$ and remains well below the present and future CMB detection threshold. However, when we project future PTA capabilities reaching upto 1 $\mu$Hz, even with our conservative estimate we find that Inflation, Scalar Induced Gravitational Waves (SIGW), and metastable cosmic strings can induce a $\Delta N_{eff}$ large enough for $>3.5\sigma$ detection by the Simons Observatory.