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

Myron Bander
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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.

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Myron Bander. 2002-05-01. An explicit time variable for cosmology and the matter-vacuum energy coincidence. https://arxiv.org/abs/gr-qc/0205006

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