  We examine the effect of the stress tensor of a quantum matter field, such as
the electromagnetic field, on the spectrum of primordial gravity waves expected
in inflationary cosmology. We find that the net effect is a small reduction in
the power spectrum, especially at higher frequencies, but which has a different
form from that described by the usual spectral index. Thus this effect has a
characteristic signature, and is in principle observable. The net effect is a
sum of two contributions, one of which is due to quantum fluctuations of the
matter field stress tensor. The other is a quantum correction to the graviton
field due to coupling to the expectation value of this stress tensor. Both
contributions are sensitive to initial conditions in the very early universe,
so this effect has the potential to act as a probe of these initial conditions.
