  Forthcoming advances in direct gravitational wave detection from kilohertz to
nanohertz frequencies have unique capabilities to detect signatures from or set
meaningful constraints on a wide range of new cosmological phenomena and new
fundamental physics. A brief survey is presented of the post-inflationary
gravitational radiation backgrounds predicted in cosmologies that include
intense new classical sources such as first-order phase transitions,
late-ending inflation, and dynamically active mesoscopic extra dimensions. LISA
will provide the most sensitive direct probes of such phenomena near TeV
energies or Terascale. LISA will also deeply probe the broadband background,
and possibly bursts, from loops of cosmic superstrings predicted to form in
current models of brane inflation.
