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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.