Canonical formulation and path integral for local vacuum energy sequestering

TL;DR

This paper develops a Hamiltonian and path integral framework for a local vacuum energy sequestering model, linking the cosmological and gravitational constants with matter energy-momentum, and introduces a topological field theory formulation.

Contribution

It provides the first Hamiltonian and path integral formulation for local vacuum energy sequestering, extending unimodular gravity and connecting constants with matter averages.

Findings

Path integral includes integrations over cosmological and gravitational constants.

Establishes a relation between constants' most likely values and matter energy-momentum.

Constructs a BRST-exact topological field theory version of the model.

Abstract

We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a BRST-exact formulation of the theory, which can be considered as a topological field theory.