A non-perturbative Hamiltonian approach to the cosmological constant problem

TL;DR

This paper explores a non-perturbative Hamiltonian approach to the cosmological constant problem, showing that vacuum energy density depends on the choice of time and is generally non-linear in the cosmological constant, thus addressing the problem.

Contribution

It develops a non-perturbative framework that relates vacuum energy to the cosmological constant through different time choices, challenging traditional formulations.

Findings

Vacuum energy density varies with time gauge choice.

In most gauges, vacuum energy density is a non-linear function of the cosmological constant.

The framework suggests the cosmological constant problem may not be well-posed.

Abstract

It was recently suggested that the cosmological constant problem as viewed in a non-perturbative framework is intimately connected to the choice of time and a physical Hamiltonian. We develop this idea further by calculating the non-perturbative vacuum energy density as a function of the cosmological constant with multiple choices of time. We also include a spatial curvature of the universe and generalize this calculation beyond cosmology at a classical level. We show that vacuum energy density depends on the choice of time, and in almost all time gauges, is a non-linear function of the cosmological constant. This non-linear relation is a calculation for the vacuum energy density given some arbitrary value of the cosmological constant. Hence, in this non-perturbative framework, the cosmological constant problem does not arise. We also discuss why the conventional cosmological constant problem is not well-posed, and formulate and answer the question: "Does vacuum gravitate?" Finally, we give a derivation of reduction to quantum mechanics on a flat background from a non-perturbative gravity-matter theory.