An explicit time variable for cosmology and the matter-vacuum energy coincidence

TL;DR

This paper proposes a new approach to cosmology by introducing an explicit time variable through vacuum expectation values, potentially explaining the observed coincidence between matter density and vacuum energy.

Contribution

It identifies a time variable in canonical general relativity using vacuum expectation values, linking energy eigenvalues to matter-vacuum energy coincidence.

Findings

Time variable can be defined via vacuum expectation values.

Energy eigenvalues influence the universe's scale parameter.

The dominant energy contribution matches observed matter and vacuum energy levels.

Abstract

By allowing for non zero vacuum expectation values for some of the fields that appear in the Hamiltonian constraint of canonical general relativity a time variable, with usual properties, can be identified; the constraint plays the role of the ordinary Hamiltonian. The energy eigenvalues contribute to the variation of the scale parameter similarly to the way matter density does. For a universe described by a superposition of eigenstates or by a thermodynamic ensemble the dominant contribution comes from energy, or equivalently effective matter density, of the same order as the vacuum energy (cosmological constant). This may explain the observed ``coincidence'' of these two values.