Cosmological fluctuations: Comparing Quantum and Classical Statistical and Stringy Effects

Abstract

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).