Implications of the NANOGrav results for inflation

The NANOGrav pulsar timing array experiment reported evidence for a stochastic common-spectrum process affecting pulsar timing residuals in its 12.5-yr data set, 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 nT and the tensor-to-scalar ratio r. Explaining NANOGrav while complying with upper limits on r from BICEP2/Keck Array and Planck requires r O(10⁻⁶) in conjunction with an extremely blue tensor spectrum, 0.7 ≲ nT ≲ 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, Tᵣₕ 100\, GeV \!-\! 1\, 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.