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Various pulsar timing array (PTA) experiments (NANOGrav, EPTA, PPTA, CPTA,including data from InPTA) very recently reported evidence for excess redcommon-spectrum signals in their latest datasets, with inter-pulsarcorrelations following the Hellings-Downs pattern, pointing to a stochasticgravitational wave background (SGWB) origin. Focusing for concreteness on theNANOGrav signal (given that all signals are in good agreement between eachother), I inspect whether it supports an inflationary SGWB explanation, findingthat such an interpretation calls for an extremely blue tensor spectrum, withspectral index $n_T \simeq 1.8 \pm 0.3$, while Big Bang Nucleosynthesis limitsrequire a very low reheating scale, $T_{\rm rh} \lesssim 10\,{\rm GeV}$. Whilenot impossible, an inflationary origin for the PTA signal is barely tenable:within well-motivated inflationary models it is hard to achieve such a bluetilt, whereas models who do tend to predict sizeable non-Gaussianities,excluded by observations. Intriguingly, ekpyrotic models naturally predict aSGWB with spectral index $n_T=2$, although with an amplitude too suppressed tobe able to explain the signal detected by PTA experiments. Finally, I provideexplicit expressions for a bivariate Gaussian approximation to the jointposterior distribution for the intrinsic-noise amplitude and spectral index ofthe NANOGrav signal, which can facilitate extending similar analyses todifferent theoretical signals.

Inflationary interpretation of the stochastic gravitational wave background signal detected by pulsar timing array experiments