  Detection of a gravitational-wave signal of non-astrophysical origin would be
a landmark discovery, potentially providing a significant clue to some of our
most basic, big-picture scientific questions about the Universe. In this white
paper, we survey the leading early-Universe mechanisms that may produce a
detectable signal -- including inflation, phase transitions, topological
defects, as well as primordial black holes -- and highlight the connections to
fundamental physics. We review the complementarity with collider searches for
new physics, and multimessenger probes of the large-scale structure of the
Universe.
