# LIV effects on the quantum stochastic motion in an acoustic FRW-geometry

**Authors:** M. A. Anacleto, C. H. G. Bessa, F. A. Brito, A. E. Mateus, E. Passos, J. R. L. Santos  
**arXiv:** [2106.09684](https://arxiv.org/abs/2106.09684)  
**Date:** 2021-06-17  
**Summary page:** https://www.summarizepaper.com/en/paper/2106.09684v1/

## Key points

- The paper explores the effects of Lorentz Invariance Violation (LIV) on the stochastic motion of scalar and massive test particles in an acoustic spatially flat Friedman-Robertson-Walker (FRW) geometry.
- Vacuum fluctuations can induce a random motion of particles, referred to as quantum Brownian motion or quantum stochastic motion.
- LIV affects this phenomenon by studying the behavior of a massless quantized scalar field on this geometry, which is derived from an Abelian Higgs model with LIV.
- It is possible to find an acoustic spatially flat FRW geometry where LI is broken in a LIV context.
- For bound particles, LIV corrections decrease their velocity dispersion and also reduce uncertainty in their motion.
- Free particles in the LIV framework exhibit null dispersion when LI is taken into account; this case is more realistic than bound particles.
- Deviations proportional to the LIV parameter are found in the velocity dispersion of particles.

## Summary

This paper explores the effects of Lorentz Invariance Violation (LIV) on the stochastic motion of scalar and massive test particles in an acoustic spatially flat Friedman-Robertson-Walker (FRW) geometry. It is well known that vacuum fluctuations can induce a random motion of particles, referred to as quantum Brownian motion or quantum stochastic motion. The authors consider how LIV affects this phenomenon by studying the behavior of a massless quantized scalar field on this geometry, which is derived from an Abelian Higgs model with LIV. In Section III, they demonstrate that it is possible to find an acoustic spatially flat FRW geometry where LI is broken, i.e., in a LIV context. In Section IV, they study the same problem described in Section II using the metric found in Section III. Comparing the results found in Sections II and IV, they observe that for bound particles, LIV corrections decrease their velocity dispersion and also reduce uncertainty in their motion. This fact can be seen from Eq. (39) and Fig. 1; note that the curve for dispersion decreases at long times. The authors also investigate the dispersion relation between sound speed at the beginning (c0) and end of expansion (csf). A change in ratio (c0/csf) causes a shift that may increase or decrease dispersion. However, they find that free particles in the LIV framework exhibit null dispersion when LI is taken into account; this case is more realistic than bound particles. Nonetheless, as shown in Eq. (46) and Fig. 2 when LIV is considered c0/csf → 1 + η5 × 10−11 - 3 × 10−10), a non-null dispersion occurs due to LIV. The most important result of this paper is that deviations proportional to the LIV parameter are found in the velocity dispersion of particles. This result provides evidence that LIV can affect quantum stochastic motion induced by vacuum fluctuations and has important implications for our understanding of fundamental physics in cosmological contexts.