Cosmological fluctuations: Comparing Quantum and Classical Statistical and Stringy Effects

TL;DR

This paper compares quantum and classical statistical interpretations of cosmological fluctuations, exploring how string theory effects and alternative pre-inflationary assumptions impact the scalar and tensor power spectra.

Contribution

It introduces a classical statistical approach to cosmological fluctuations, replacing the quantum vacuum, and examines the implications of string theory scales on inflationary predictions.

Findings

Classical statistical distributions can replicate quantum fluctuation calculations.

Replacing Planck length with string scale alters the inflation-scalar spectrum relation.

Differences emerge at higher loop orders and in models with low sound speed or dissipation.

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).