A natural origin of primordial density perturbations

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We suggest here a mechanism for the seeding of the primordial density fluctuations. We point out that a process like reheating at the end of inflation will inevitably generate perturbations, even on superhorizon scales, by the local diffusion of energy. Provided that the final temperature is of order the GUT scale, the density contrast $\delta_R$ for spheres of radius $R$ will be of order $10^{-5}$ at horizon entry, consistent with the values measured by \texttt{WMAP}. If this were a purely classical process, $\delta_R^2$ would fall as $1/R^4$ beyond the horizon, and the resulting primordial density power spectrum would be $P(k) \propto k^n$ with $n=4$. However, as shown by Gabrielli et al, a quantum diffusion process can generate a power spectrum with any index in the range $0<N\LEQ $n="1$" for R^4$ $1 and $n<1$ R^{3+n}$ 1 $\propto be then will ($\delta_R^2$ observed the to close values including 4$,>1$). Thus, the two characteristic parameters that determine the appearance of present day structures could be natural consequences of this mechanism. These are in any case the minimum density variations that must have formed if the universe was rapidly heated to GUT temperatures by the decay of a `false vacuum'. There is then no \emph{a priori} necessity to postulate additional (and fine tuned) quantum fluctuations in the `false vacuum', nor a pre-inflationary period. Given also the very stringent pre-conditions required to trigger a satisfactory period of inflation, altogether it seems at least as natural to assume that the universe began in a flat and homogeneously expanding phase.