Lagrangian Formulation of a Solution to the Cosmological Constant Problem

Abstract

A covariant Lagrangian formulation of a solution to the cosmological constant problem, based on vizualising the fluctuations of the vacuum energy as a non-equilibrium process with stochastic behaviour, is presented. The variational principle yields equations of motion for the cosmological ``constant" $Λ$, treated as a dynamical field, together with an equation for a Lagrange multiplier field $ϕ$, and the standard Einstein field equations with a variable cosmological constant term. A stochastic model of $Λ$ yields a natural explanation for the smallness or zero value of the constant in the present epoch and its large value in an era of inflation in the early universe.

Typeset using Revtex. 7 pages. No figures