Implications of the NANOGrav results for inflation

Abstract

The NANOGrav pulsar timing array experiment reported evidence for a stochastic common-spectrum process affecting pulsar timing residuals in its 12.5-year dataset, which might be interpreted as the first detection of a stochastic gravitational wave background (SGWB). I examine whether the NANOGrav signal might be explained by an inflationary SGWB, focusing on the implications for the tensor spectral index $n_T$ and the tensor-to-scalar ratio $r$. Explaining NANOGrav while complying with upper limits on $r$ from BICEP2/Keck Array and Planck requires $r\gtrsim \mathcal{O}(10^{-6})$ in conjunction with an extremely blue tensor spectrum, $0.7\lesssim n_T\lesssim 1.3$. After discussing models which can realize such a blue spectrum, I show that this region of parameter space can be brought in agreement with Big Bang Nucleosynthesis constraints for a sufficiently low reheating scale, $T_{\mathrm{rh}}\lesssim 100\mathrm{GeV}-1\mathrm{TeV}$. With the important caveat of having assumed a power-law parametrization for the primordial tensor spectrum, an inflationary interpretation of the NANOGrav signal is therefore not excluded.

5 pages, 2 figures. v2: revised conclusions, NANOGrav can in principle be due to an inflationary SGWB provided the reheating temperature is sufficiently (=very) low. References added, version accepted for publication in MNRAS Letters. Comments are welcome

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