  We systematically investigate the effect of short distance physics on the
spectrum of temperature anistropies in the Cosmic Microwave Background produced
during inflation. We present a general argument-assuming only low energy
locality-that the size of such effects are of order H^2/M^2, where H is the
Hubble parameter during inflation, and M is the scale of the high energy
physics.
  We evaluate the strength of such effects in a number of specific string and M
theory models. In weakly coupled field theory and string theory models, the
effects are far too small to be observed. In phenomenologically attractive
Horava-Witten compactifications, the effects are much larger but still
unobservable. In certain M theory models, for which the fundamental Planck
scale is several orders of magnitude below the conventional scale of grand
unification, the effects may be on the threshold of detectability.
  However, observations of both the scalar and tensor fluctuation contributions
to the Cosmic Microwave Background power spectrum-with a precision near the
cosmic variance limit-are necessary in order to unambiguously demonstrate the
existence of these signatures of high energy physics. This is a formidable
experimental challenge.
