Semiclassicality and Decoherence of Cosmological Perturbations

Details Semiclassicality and Decoherence of Cosmological Perturbations Semiclassicality and Decoherence of Cosmological Perturbations

1995-04-20

arxiv.org/abs/gr-qc/9504030v2

Class.Quant.Grav.13:377-392,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revised version to appear in Class. Quantum Grav. All prior conclusions hold. This version contains in particular a Wigner fun

Scientific paper

10.1088/0264-9381/13/3/006

Transition to the semiclassical behaviour and the decoherence process for inhomogeneous perturbations generated from the vacuum state during an inflationary stage in the early Universe are considered both in the Heisenberg and the Schr\"odinger representations to show explicitly that both approaches lead to the same prediction: the equivalence of these quantum perturbations to classical perturbations having stochastic Gaussian amplitudes and belonging to the quasi-isotropic mode. This equivalence and the decoherence are achieved once the exponentially small (in terms of the squeezing parameter $r_k$) decaying mode is neglected. In the quasi-classical limit $|r_k|\to \infty$, the perturbation mode functions can be made real by a time-independent phase rotation, this is shown to be equivalent to a fixed relation between squeezing angle and phase for all modes in the squeezed-state formalism. Though the present state of the gravitational wave background is not a squeezed quantum state in the rigid sense and the squeezing parameters loose their direct meaning due to interaction with the environment and other processes, the standard predictions for the rms values of the perturbations generated during inflation are not affected by these mechanisms (at least, for scales of interest in cosmological applications). This stochastic background still occupies a small part of phase space.

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