  Various pulsar timing array (PTA) experiments (NANOGrav, EPTA, PPTA, CPTA,
including data from InPTA) very recently reported evidence for excess red
common-spectrum signals in their latest datasets, with inter-pulsar
correlations following the Hellings-Downs pattern, pointing to a stochastic
gravitational wave background (SGWB) origin. Focusing for concreteness on the
NANOGrav signal (given that all signals are in good agreement between each
other), I inspect whether it supports an inflationary SGWB explanation, finding
that such an interpretation calls for an extremely blue tensor spectrum, with
spectral index $n_T \simeq 1.8 \pm 0.3$, while Big Bang Nucleosynthesis limits
require a very low reheating scale, $T_{\rm rh} \lesssim 10\,{\rm GeV}$. While
not impossible, an inflationary origin for the PTA signal is barely tenable:
within well-motivated inflationary models it is hard to achieve such a blue
tilt, whereas models who do tend to predict sizeable non-Gaussianities,
excluded by observations. Intriguingly, ekpyrotic models naturally predict a
SGWB with spectral index $n_T=2$, although with an amplitude too suppressed to
be able to explain the signal detected by PTA experiments. Finally, I provide
explicit expressions for a bivariate Gaussian approximation to the joint
posterior distribution for the intrinsic-noise amplitude and spectral index of
the NANOGrav signal, which can facilitate extending similar analyses to
different theoretical signals.
