  Several pulsar-timing array (PTA) collaborations are finding tantalising
hints for a stochastic gravitational wave background signal in the nano-Hertz
regime. So far, though, no convincing evidence for the expected Hellings-Downs
quadrupolar correlations has been found. While this issue might get fixed at
the light of more accurate, forthcoming data, it is important to keep an eye
open on different possibilities, and explore scenarios able to produce
different types of PTA angular correlations. We point out that a stationary
non-Gaussian component to the gravitational wave background can modulate the
2-point PTA overlap reduction function, adding contributions that can help in
fitting the angular distribution of PTA data. We discuss possible sources for
such non-Gaussian signal in terms of cosmological processes occurring after
inflation ends, and we investigate further tests for this idea.
