Stochastic String Topography and Multivacua

TL;DR

This paper models the string landscape using stochastic equations to explore how vacuum fluctuations might explain the small positive cosmological constant observed in our universe.

Contribution

It introduces a stochastic Langevin framework for string topography and derives a Focker-Planck equation to analyze multivacua in string/M-theory.

Findings

Stochastic fluctuations can produce a small positive cosmological constant.

The model describes non-supersymmetric multivacua in string theory.

Probabilistic landscape of vacua is characterized mathematically.

Abstract

The suggestion that there exist causally disconnected universes or sub-universes to explain the values of physical parameters such as the cosmological constant is discussed. A statistical model of the string landscape/topography is formulated using a stochastic Langevin equation for string and supergravity potentials. A Focker-Planck equation for the probability density of superpotentials is derived and the possible non-supersymmetric multivacua describing string/M-theory topography are investigated. The stochastic fluctuations of the superpotentials and their associated vacuum states can possibly lead to a small positive cosmological constant.