Disentangling the origins of the NANOGrav signal: Early Universe models and ΔN_eff bounds

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, ΔN_eff, for a number of Early-Universe models proposed to explain the pulsar timing array (PTA) spectrum. We demonstrate that models predicting ΔN_eff above the CMB limit would either be excluded or require a significant additional contribution from other sources to explain the NANOGrav signal while remaining consistent with the CMB constraints. We find that current NANOGrav 15-year dataset, sensitive up to 60 nHz, gives a negligible contribution to ΔN_eff and remains well below the present and future CMB detection threshold. However, when we project future PTA capabilities reaching upto 1 μHz, even with our conservative estimate we find that Inflation, Scalar Induced Gravitational Waves (SIGW), and metastable cosmic strings can induce a ΔN_eff large enough for >3.5σ detection by the Simons Observatory.