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The theory of cosmological fluctuations assumes that the pre-inflationarystate of the universe was the quantum vacuum of a scalar field(s) coupled togravity. The observed cosmic microwave background fluctuations are theninterpreted as quantum fluctuations. Here we consider alternate interpretationsof the classic calculations of scalar and tensor power spectra by replacing theBunch-Davies quantum vacuum with a classical statistical distribution, whichmay have been the consequence of a pre-inflationary process of decoherence asin the quantum cosmology literature. Mathematically they are essentiallyidentical calculations. However if one takes the latter interpretation then onemight replace the Planck length by for instance the fundamental length scale ofstring theory. In particular this changes the relation between the scale ofinflation and the scalar power spectrum but leaves the parameter(s)characterizing the bi-spectrum unchanged at leading order. Differences willoccur however at higher order in the loop expansion. We also discuss therelation to theories with low sound speed and/or a period of dissipation duringinflation (warm inflation).

Cosmological fluctuations: Comparing Quantum and Classical Statistical and Stringy Effects