Canonical formulation and path integral for local vacuum energy sequestering

Understand

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.