Time dependent fluctuations and particle production in cosmological de Sitter and anti-de Sitter spaces

TL;DR

This paper investigates the evolution of fluctuations and particle production in expanding de Sitter and contracting anti-de Sitter universes using the functional Schrödinger formalism, revealing distinct behaviors and potential cosmological implications.

Contribution

It introduces a novel application of the functional Schrödinger formalism to study time-dependent fluctuations in cosmological spaces, surpassing standard approximation methods.

Findings

Fluctuation frequencies diminish in expanding dS space, leading to thermal radiation.

Fluctuation frequencies grow in contracting AdS space, with diverging temperature near the Big Crunch.

Oscillations in the spectrum make the temperature ill-defined, indicating instability.

Abstract

We study the evolution of time-dependent fluctuations and particle production in an expanding dS and contracting AdS universe. Using the functional Schrodinger formalism we are able to probe the time dependent regime which is out of the reach of the standard approximations like the Bogolyubov method. In both cases, the evolution of fluctuations is governed by the harmonic oscillator equation with time dependent frequency. In the case of an expanding dS universe we explicitly show that the frequency of fluctuations produced at a certain moment diminish in time, while the distribution of the created particles quickly approaches the thermal radiation of the dS space. In the case of a contracting AdS universe we show that the frequency of fluctuations produced at a certain moment grow in time. Nominally, the temperature of radiation diverges as the Big Crunch is approaching, however, increasing oscillations of the spectrum make the temperature poorly defined, which is in agreement with the fact that AdS space does not have an event horizon which would cause thermal radiation. Unlimited growth of fluctuations indicates that an eventual tunneling into AdS vacuum would have catastrophic consequences for our universe.