143 research outputs found
Cosmological perturbations from stochastic gravity
In inflationary cosmological models driven by an inflaton field the origin of
the primordial inhomogeneities which are responsible for large scale structure
formation are the quantum fluctuations of the inflaton field. These are usually
computed using the standard theory of cosmological perturbations, where both
the gravitational and the inflaton fields are linearly perturbed and quantized.
The correlation functions for the primordial metric fluctuations and their
power spectrum are then computed. Here we introduce an alternative procedure
for computing the metric correlations based on the Einstein-Langevin equation
which emerges in the framework of stochastic semiclassical gravity. We show
that the correlation functions for the metric perturbations that follow from
the Einstein-Langevin formalism coincide with those obtained with the usual
quantization procedures when the scalar field perturbations are linearized.
This method is explicitly applied to a simple model of chaotic inflation
consisting of a Robertson-Walker background, which undergoes a quasi-de-Sitter
expansion, minimally coupled to a free massive quantum scalar field. The
technique based on the Einstein-Langevin equation can, however, deal naturally
with the perturbations of the scalar field even beyond the linear
approximation, as is actually required in inflationary models which are not
driven by an inflaton field such as Starobinsky's trace-anomaly driven
inflation or when calculating corrections due to non-linear quantum effects in
the usual inflaton driven models.Comment: 29 pages, REVTeX; minor changes, additional appendix with an
alternative proof of the equivalence between stochastic and quantum
correlation functions as well as an exact argument showing that the
correlation function of curvature perturbations remains constant in time for
superhorizon modes, which clarifies a recent claim in arXiv:0710.5342v
Stochastic description for open quantum systems
A linear open quantum system consisting of a harmonic oscillator linearly
coupled to an infinite set of independent harmonic oscillators is considered;
these oscillators have a general spectral density function and are initially in
a Gaussian state. Using the influence functional formalism a formal Langevin
equation can be introduced to describe the system's fully quantum properties
even beyond the semiclassical regime. It is shown that the reduced Wigner
function for the system is exactly the formal distribution function resulting
from averaging both over the initial conditions and the stochastic source of
the formal Langevin equation. The master equation for the reduced density
matrix is then obtained in the same way a Fokker-Planck equation can always be
derived from a Langevin equation characterizing a stochastic process. We also
show that a subclass of quantum correlation functions for the system can be
deduced within the stochastic description provided by the Langevin equation. It
is emphasized that when the system is not Markovian more information can be
extracted from the Langevin equation than from the master equation.Comment: 16 pages, RevTeX, 1 figure (uses epsf.sty). Shortened version.
Partially rewritten to emphasize those aspects which are new. Some references
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