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

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.

8 pages, 6 figures

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• Time dependent particle production and particle number in cosmological de Sitter space
• Hawking-like radiation and the density matrix for an infalling observer during gravitational collapse
• Instability of Quantum de Sitter Spacetime
• Gravitational collapse and Hawking-like radiation of the shell in AdS spacetime
• Quantum Dynamics for de Sitter Radiation
• Gravitational systems in asymptotically anti-de Sitter space-times
• Time Evolution of Temperature and Entropy of Various Collapsing Domain Walls
• Induced energy-momentum tensor of Dirac field in 2D de Sitter QED
• Volume Renormalization and the Higgs