Hamiltonian reduction of Bianchi Cosmologies

TL;DR

This paper proposes a new approach to Bianchi cosmologies by deriving a constraint from a restricted action principle, which generates all homogeneity-preserving diffeomorphisms and clarifies the automorphism structure.

Contribution

It introduces an alternative to the ADM constraint for Bianchi models, enabling a complete generation of homogeneity-preserving diffeomorphisms from a restricted action.

Findings

The new constraint generates all homogeneity-preserving diffeomorphisms.

Automorphism generating vector fields are identified in class A and B models.

The approach aligns with Dirac's formalism, focusing on the unimodular automorphism subgroup.

Abstract

It was noted recently that the ADM-diffeomorphism-constraint does not generate all observed symmetries for several Bianchi-models. We will suggest not to use the ADM-constraint restricted to homogeneous variables, but some equivalent which is derived from a restricted action principle. This will generate all homogeneity preserving diffeomorphisms, which will be shown to be automorphism generating vector fields, in class A and class B models. Following Dirac's constraint formalism one will naturally be restricted to the unimodular part of the automorphism group.