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

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, $\hat{I}”N_{eff}$, for a number of Early-Universe models proposed to explain the pulsar timing array (PTA) spectrum. We demonstrate that models predicting $\hat{I}”N_{eff}$ 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 $\hat{I}”N_{eff}$ and remains well below the present and future CMB detection threshold. However, when we project future PTA capabilities reaching upto 1 $\hat{I}¼$Hz, even with our conservative estimate we find that Inflation, Scalar Induced Gravitational Waves (SIGW), and metastable cosmic strings can induce a $\hat{I}”N_{eff}$ large enough for $>3.5\ddot{I}ƒ$ detection by the Simons Observatory.

26 pages, 3 figures, and 3 tables. Comments are welcome