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.

Vacuum fluctuations of a scalar field near a reflecting boundary and their effects on the motion of a test particle

“…for the dispersion of the velocity in the direction parallel (x and y directions) to the wall. When some parameters are conveniently chosen, the above results coincide with the dispersions calculated for a free particle near a reflecting boundary in an analog FRW spacetime [19]. Notice that in both directions the dispersions diverge at z = 0 and τ = 2z.…”

“…Quantum dispersions induced by vacuum fluctuations of a scalar field in an analog model for Friedmann-Robertson-Walker (FRW) spatially flat spacetime were recently studied in the context of an expanding Bose-Einstein condensate [19]. As a result it was claimed that implementing a time dependent scale factor is enough to regularize the divergences that appear when one reflecting boundary is present, and thus it would play the same role of a smooth switching function in the regularization process.…”

Brownian motion and polarized three-dimensional quantum vacuum

“…In other words we can say that, in our model, the equilibrium dispersion emerges as a collective property which is generated by the fundamental frequencies of the 3D quantum vacuum, given by (41).…”

Induced Brownian motion by the Friedmann–Robertson–Walker spacetime in the presence of a cosmic string

“…As before, we can also obtain an analytic expression for the approximation R 1 considering (26) only for integer values of p. In this case, there is only the first term on the r.h.s of (26), so that the approximated expression (28) can be used to obtain…”

“…This is similar to the one found in Refs. [10,11,28]. For instance, taking p = 4 as shown in as a function of the dimensionless radial distance R = 2ρ cη , considering p = 4.…”