  We present an in depth discussion of the production of gravitational waves
from an inflationary phase that could have occurred in the early universe,
giving derivations for the resulting spectrum and energy density. We also
consider the large-scale anisotropy in the cosmic microwave background
radiation coming from these waves. Assuming that the observed quadrupole
anisotropy comes mostly from gravitational waves (consistent with the
predictions of a flat spectrum of scalar density perturbations and the measured
dipole anisotropy) we describe in detail how to derive a value for the scale of
inflation of $(1.5-5)\times 10^{16}$GeV, which is at a particularly interesting
scale for particle physics. This upper limit corresponds to a 95\% confidence
level upper limit on the scale of inflation assuming only that the quadrupole
anisotropy from gravitational waves is not cancelled by another source. Direct
detection of gravitational waves produced by inflation near this scale will
have to wait for the next generation of detectors.
