Hamilton-Jacobi method for Domain Walls and Cosmologies

TL;DR

This paper employs Hamiltonian methods to derive first order equations for curved domain walls and cosmologies, analyzing their stability, supersymmetry, and wave-function in a unified framework.

Contribution

It introduces a Hamilton-Jacobi approach to study domain walls and cosmologies, providing new insights into their stability, supersymmetry, and quantum wave-function.

Findings

Recovered supersymmetry conditions for Minkowski and AdS-sliced domain walls.

Showed stability of domain walls despite AdS vacuum instabilities.

Computed the wave-function of a closed universe approaching de Sitter space.

Abstract

We use Hamiltonian methods to study curved domain walls and cosmologies. This leads naturally to first order equations for all domain walls and cosmologies foliated by slices of maximal symmetry. For Minkowski and AdS-sliced domain walls (flat and closed FLRW cosmologies) we recover a recent result concerning their (pseudo)supersymmetry. We show how domain-wall stability is consistent with the instability of adS vacua that violate the Breitenlohner-Freedman bound. We also explore the relationship to Hamilton-Jacobi theory and compute the wave-function of a 3-dimensional closed universe evolving towards de Sitter spacetime.