Five-dimensional scenario with a fluctuating three-brane: an stochastic approach to gravity

TL;DR

This paper proposes a five-dimensional model with a fluctuating three-brane, using stochastic methods to address gravity, the mass hierarchy, and the cosmological constant problem, linking these issues through the stochastic nature of gravity.

Contribution

It introduces a stochastic approach to gravity in a five-dimensional scenario with a fluctuating brane, providing new insights into longstanding fundamental problems.

Findings

The model accounts for the mass hierarchy problem.

It offers a novel treatment of the cosmological constant problem.

In the no-fluctuation limit, it reduces to thin-brane scenarios.

Abstract

A five-dimensional scenario with a non compact extra dimension of infinite extent is studied, in which a single three-brane is affected by small Gaussian fluctuations in the extra dimension. The average magnitude of the fluctuations is of order of the electro-weak length scale ($\sigma\sim m_{EW}^{-1}$). The model provides an stochastic approach to gravity that accounts for an alternative resolution of the mass hierarchy problem. The cosmological constant problem can be suitably treated as well. Surprisingly the Mach's principle finds a place in the model. It is argued that the Mach's principle, the mass hierarchy and the cosmological constant problem, are different aspects of a same property of gravity in this model: its stochastic character. Thin-brane scenarios are recovered in the "no-fluctuations" limit ($\sigma\to 0$).