Quantum Modifications to Gravity Waves in de Sitter Spacetime
  We treat a model in which tensor perturbations of de~Sitter spacetime,
represented as a spatially flat model, are modified by the effects of the
vacuum fluctuations of a massless conformally invariant field, such as the
electromagnetic field. We use the semiclassical theory of gravity with the
expectation value of the conformal field stress tensor as a source. We first
study the stability of de~Sitter spacetime by searching for growing, spatially
homogeneous modes, and conclude that it is stable within the limits of validity
of the semiclassical theory. We next examine the modification of linearized
plane gravity waves by the effects of the quantum stress tensor. We find a
correction term which is of the same form as the original wave, but displaced
in phase by -\pi/2, and with an amplitude which depends upon the duration of
inflation. The magnitude of this effect is proportional to the change in scale
factor during inflation. So long as the energy scale of inflation and the
proper frequency of the mode at the beginning of inflation are well below the
Planck scale, the fractional correction is small. However, modes which are
transplanckian at the onset of inflation can undergo a significant correction.
The increase in amplitude can potentially have observable consequences through
a modification of the power spectrum of tensor perturbations in inflationary
cosmology. This enhancement of the power spectrum depends upon the duration of
inflation and is greater for shorter wavelengths.
