  We discuss the interpretation of the detected signal by Pulsar Timing Array
(PTA) observations as a gravitational wave background (GWB) of cosmological
origin. We combine NANOGrav 15-years and EPTA-DR2new data sets and confront
them against backgrounds from supermassive black hole binaries (SMBHBs), and
cosmological signals from inflation, cosmic (super)strings, first-order phase
transitions, Gaussian and non-Gaussian large scalar fluctuations, and audible
axions. We find that scalar-induced, and to a lesser extent audible axion and
cosmic superstring signals, provide a better fit than SMBHBs. These results
depend, however, on modeling assumptions, so further data and analysis are
needed to reach robust conclusions. Independently of the signal origin, the
data strongly constrain the parameter space of cosmological signals, for
example, setting an upper bound on primordial non-Gaussianity at PTA scales as
$|f_{nl}| \lesssim 2.34$ at 95% CL.
