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

## TL;DR

This paper investigates how quantum vacuum fluctuations influence scalar particles in an analog Friedmann-Robertson-Walker universe, showing that particles undergo Brownian motion and discussing potential experimental detection using Bose-Einstein condensates.

## Contribution

It introduces a model for quantum scalar field effects in an analog cosmological setting, analyzing boundary effects and proposing experimental implementation with Bose-Einstein condensates.

## Key findings

- Particles exhibit Brownian motion due to vacuum fluctuations.
- Boundary effects can be regularized in an expanding universe.
- Potential for experimental detection in Bose-Einstein condensates.

## 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.