Large pre-inflationary thermal density perturbations
  In some versions of the theory of inflation, it is assumed that before
inflation began the universe was in a Friedmann-Robertson-Walker (FRW) stage,
with the energy density dominated by massless particles. The origin of the
nearly scale-invariant density perturbations is quantum fluctuations in the
inflaton field. Here we point out that under those conditions there would
necessarily also be large thermally induced density perturbations. It is
asserted that inflation would smooth out any pre-existing perturbations. But
that argument relies on linear perturbation theory of the scalar modes, which
would be rendered invalid because of the non-negligibility of the vector and
tensor modes when the perturbation in the total density becomes large. Under
those circumstances the original proof that inflation would have the desired
smoothing effect no longer applies, {\it i.e.} for the theory to be robust an
alternative (and hitherto unavailable) demonstration of the smoothing that
takes account of these non-linear terms is necessary.
