Quantum fluctuations in the open universe

TL;DR

This paper resolves a controversy about the role of exponential modes in quantum density fluctuations in open universes, providing exact calculations and extending the analysis to general open FRW models.

Contribution

It rigorously demonstrates the physical relevance of exponential modes in quantum fields in open universes and calculates the power spectrum for any mass without divergences.

Findings

Exponential modes are physically relevant in quantum fluctuations.

These modes cause de Sitter symmetry breaking for massless fields.

An exact, divergence-free power spectrum is derived for all masses.

Abstract

We solve a continuing controversy when dealing with density fluctuations in open Friedman-Robertson-Walker universes, on the physical relevance of a class of exponential modes. We show explicitly and rigorously that these modes enter the expansion of quantum fields. In the maximally symmetric de Sitter case, encountered in inflationary models, they are excited for fields with mass below a critical value. They are seen to be responsible for the breaking of the de Sitter symmetry for a massless field. We provide an exact calculation of the power spectrum for any mass. Our method is free of the divergences that appear in earlier treatments. We extend the construction to a generic open FRW universe.