[Paper Review] On the quantitative calculation of the cosmological constant of the quantum vacuum

Hongwei Xiong|arXiv (Cornell University)|May 26, 2018

Cosmology and Gravitation Theories11 references4 citations

TL;DR

This paper proposes a quantum cosmological model where the universe's wave function is a superposition of states with different cosmological constants, arising from vacuum quantum fluctuations and quasi-thermal equilibrium. Using Everett’s relative-state formulation and density matrix formalism, it derives a theoretical value of ΩΛ ≈ 68.85% for dark energy density relative to critical density—remarkably close to the observed 68.5%—without any fitting parameters.

ABSTRACT

It is widely believed that as one of the candidates for dark energy, the cosmological constant should relate directly with the quantum vacuum. Despite decades of theoretical effects, however, there is still no quantitative interpretation of the observed cosmological constant. In this work, we consider the quantum state of the whole universe including the quantum vacuum. Everett's relative-state formulation, vacuum quantum fluctuations and the validity of Einstein's field equation at macroscopic scales imply that our universe wave function might be a superposition of states with different cosmological constants. In the density matrix formulation of this quantum universe, the quasi-thermal equilibrium state is described by a specific cosmological constant with the maximum probability. Without any fitting parameter, the ratio between the vacuum energy density due to the cosmological constant (dark energy) and the critical density of the universe is 68.85% based on simple equations in our theoretic model, which agrees very well with the best current astronomical observations of 68.5%.

Motivation & Objective

• To resolve the fine-tuning and coincidence problems of dark energy by providing a quantitative quantum mechanical explanation for the cosmological constant.
• To extend the wave function of the universe to include the quantum vacuum, treating it as a superposition of states with different cosmological constants.
• To derive the cosmological constant using the principle of quasi-thermal equilibrium between the quantum vacuum and matter/radiation contents.
• To achieve a parameter-free prediction of the dark energy density fraction that matches current astronomical observations.

Proposed method

• Adopt Everett’s relative-state formulation to describe the universe as a quantum superposition of states with varying cosmological constants.
• Model the quantum vacuum using vacuum energy fluctuations and assume spontaneous symmetry breaking due to inter-vacuum correlations.
• Construct a density matrix for the quantum universe to describe the statistical state of the system.
• Apply the quasi-thermal equilibrium condition between the quantum vacuum and matter/radiation to determine the most probable cosmological constant.
• Use the energy density balance between vacuum, matter, and radiation to compute the dark energy fraction ΩΛ numerically.
• Neglect radiation contribution for low redshifts, simplifying the calculation to focus on matter and vacuum energy dominance.

Experimental results

Research questions

• RQ1 Can the cosmological constant be derived quantitatively from quantum vacuum fluctuations without fitting parameters?
• RQ2 How does the superposition of cosmological constant states in the universal wave function lead to a preferred value for the observed dark energy density?
• RQ3 What role does quasi-thermal equilibrium between the quantum vacuum and matter/radiation play in selecting the most probable cosmological constant?
• RQ4 Why does the theoretical prediction of ΩΛ ≈ 68.85% closely match the observed value of 68.5%?
• RQ5 How does the initial quantum vacuum state evolve into a universe with a stable, observed dark energy fraction?

Key findings

• The model predicts a dark energy density fraction of ΩΛ ≈ 68.85%, which is in excellent agreement with the observed value of 68.5% from astronomical data.
• The result is achieved without any fitting parameters, indicating a strong theoretical consistency with current observations.
• The cosmological constant with maximum probability emerges from the quasi-thermal equilibrium condition between the quantum vacuum and the material contents of the universe.
• The vacuum energy fluctuations are suppressed due to inter-vacuum correlations, resolving the problem of divergent energy scales at the Planck scale.
• The model suggests that the dark energy fraction remains constant across cosmic time, even as energy densities evolve, due to the universal nature of the derived value.
• The initial quantum vacuum state evolves through an inflationary stage followed by a quasi-thermal equilibrium stage, leading to the observed cosmic structure and dark energy dominance.