  The theory of cosmological fluctuations assumes that the pre-inflationary
state of the universe was the quantum vacuum of a scalar field(s) coupled to
gravity. The observed cosmic microwave background fluctuations are then
interpreted as quantum fluctuations. Here we consider alternate interpretations
of the classic calculations of scalar and tensor power spectra by replacing the
Bunch-Davies quantum vacuum with a classical statistical distribution, which
may have been the consequence of a pre-inflationary process of decoherence as
in the quantum cosmology literature. Mathematically they are essentially
identical calculations. However if one takes the latter interpretation then one
might replace the Planck length by for instance the fundamental length scale of
string theory. In particular this changes the relation between the scale of
inflation and the scalar power spectrum but leaves the parameter(s)
characterizing the bi-spectrum unchanged at leading order. Differences will
occur however at higher order in the loop expansion. We also discuss the
relation to theories with low sound speed and/or a period of dissipation during
inflation (warm inflation).
