A Non-perturbative Hamiltonian Approach to the Cosmological Constant Problem

Foundations of Physics 49 (5):391-427 (2019)
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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, certain conventional aspects of the cosmological constant problem do not arise. We also discuss why the conventional cosmological constant problem is not well-posed, and formulate and answer the question: “Does vacuum gravitate?”

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Problems with the cosmological constant problem.Adam Koberinski - 2021 - In Christian Wüthrich, Baptiste Le Bihan & Nick Huggett, Philosophy Beyond Spacetime: Implications From Quantum Gravity. Oxford: Oxford University Press.
The quantum vacuum and the cosmological constant problem.Svend E. Rugh & Henrik Zinkernagel - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (4):663-705.
Lambda: The Constant That Refuses to Die.John Earman - 2001 - Archive for History of Exact Sciences 55 (3):189-220.
The quantum vacuum and the cosmological constant problem.Svend E. Rugh & Henrik Zinkernagel - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (4):663-705.

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