  In recent years, several pulsar timing array collaborations have reported
first hints for a stochastic gravitational wave background at nano-Hertz
frequencies. Here we elaborate on the possibility that this signal comes from
new physics that leads to the generation of a primordial stochastic
gravitational wave background. We propose a set of simple but concrete models
that can serve as benchmarks for gravitational waves sourced by cosmological
phase transitions, domain wall networks, cosmic strings, axion dynamics, or
large scalar fluctuations. These models are then confronted with pulsar timing
data and with cosmological constraints. With only a limited number of free
parameters per model, we are able to identify viable regions of parameter space
and also make predictions for future astrophysical and laboratory tests that
can help with model identification and discrimination.
