  The energy density correlation function $C(x,y)=<\rho(x)\rho(y)>-<\rho>^2$
and its Fourier transform generated by the gravitational tidal forces of the
inflationary de Sitter expansion are derived for a massless or light ($m<<H$)
neutral scalar field $\Phi$ without self--interactions, minimally coupled to
gravity. The field has no classical background component, $<\Phi>=0$. Every
observationally relevant mode (which has today $\lambda_{phys}<H_0^{-1}$) had
at early times $R/k_{phys}^2\to0$, and is taken to be initially in the
Minkowski vacuum state. Our computation of $C(x,y)$, which involves four field
operators, is finite and unambiguous at each step, since we use the following
two tools: (1) We use a normal ordered energy density operator N$[\rho]$ and
show that any normal ordering N gives the same finite result. (2) Since
$C(x,y)$ has the universal $|x-y|^{-8}$ short--distance behaviour, the Fourier
transform can only be performed after smearing the energy density operator in
space and time with a smearing scale $\tau$. The resulting energy density
fluctuations are non--Gaussian, but obey a $\chi^2$--distribution. The power
spectrum $\dk$ involves a smearing scale $\tau$, and we choose $\tau=k^{-1}$.
For massless scalars we obtain $k^3\dk\sim H^4k^4$ on super--horizon scales
$k<H$. For light scalars with masses $m\ll H$ a plateau appears on the largest
scales $k<\sqrt{m^3/H}$, the result is $k^3\dk\sim m^6H^2(k/H)^{4m^2/3H^2}$. On
sub--horizon scales $k>H$ we have the universal law $k^3\dk\sim k^8$.
