  Perturbative quantum corrections to primordial power spectra are important
for testing the robustness and the regime of validity of inflation as an
effective field theory. Although this has been done extensively for the density
power spectrum (and, to some extent, for the tensor spectrum) using loop
corrections, we do so in an open quantum system approach to the problem.
Specifically, we calculate the first order corrections to the primordial
gravitational wave spectrum due to (cubic) tensor interactions alone. We show
that our results match expectations from standard loop corrections only in the
strict Markovian limit, and therefore, establish a systematic way to relax this
approximation in the future, as is generally necessary for gravitational
systems.
