Quantum Brownian motion in an analog Friedmann-Robertson-Walker geometry

Abstract

In this paper we study the effects of quantum scalar field vacuum fluctuations on scalar test particles in an analog model for the Friedmann-Robertson-Walker spatially flat geometry. In this scenario, the cases with one and two perfectly reflecting plane boundaries are considered as well the case without boundary. We find that the particles can undergo Brownian motion with a nonzero mean squared velocity induced by the quantum vacuum fluctuations due to the time dependent background and the presence of the boundaries. Typical singularities which appears due to the presence of the boundaries in flat spacetime can be naturally regularized for an asymptotically bounded expanding scale function. Thus, shifts in the velocity could be, at least in principle, detectable experimentally. The possibility to implement this observation in an analog cosmological model by the use of a Bose-Einstein condensate is also discussed.

26 pages, 7 figures. Accepted for Publication in Phys. Rev. D

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• Quantum Brownian motion for a particle in analog expanding cosmologies in the presence of disclination
• Quantum Brownian motion induced by an inhomogeneous tridimensional space and a $S^1\times R^3$ topological space-time
• LIV effects on the quantum stochastic motion in an acoustic FRW-geometry