The Geometrical Origin of Dark Energy

Abstract

The geometrical formulation of the quantum Hamilton-Jacobi theory shows that the quantum potential is never trivial, so that it plays the rôle of intrinsic energy. Such a key property selects the Wheeler-DeWitt (WDW) quantum potential $Q[g_{jk}]$ as the natural candidate for the dark energy. This leads to the WDW Hamilton-Jacobi equation with a vanishing kinetic term, and with the identification $$\Lambda =-\frac{{\kappa }^2}{\sqrt{\bar{g}}}Q[g_{jk}].$$ This shows that the cosmological constant is a quantum correction of the Einstein tensor, reminiscent of the von Weizsäcker correction to the kinetic term of the Thomas-Fermi theory. The quantum potential also defines the Madelung pressure tensor. The geometrical origin of the vacuum energy density, a strictly non-perturbative phenomenon, provides strong evidence that it is due to a graviton condensate. Time independence of the regularized WDW equation suggests that the ratio between the Planck length and the Hubble radius may be a time constant, providing an infrared/ultraviolet duality. We speculate that such a duality is related to the local to global geometry theorems for constant curvatures, showing that understanding the universe geometry is crucial for a formulation of Quantum Gravity.

arXiv commentComments and references added. Typos corrected. 20 pages

References in corpus (26)

• The Cosmological Constant
• The Dynamics of General Relativity
• Effective Field Theory, Black Holes, and the Cosmological Constant
• The fundamental constants and their variation: observational status and theoretical motivations
• Varying constants, Gravitation and Cosmology
• Cosmological constant and vacuum energy: old and new ideas
• New constraints on time-dependent variations of fundamental constants using Planck data
• The Equivalence Postulate of Quantum Mechanics
• Equivalence Principle, Higher Dimensional Moebius Group and the Hidden Antisymmetric Tensor of Quantum Mechanics
• Dark matter and dark energy from Bose-Einstein condensate
• Quantum Mechanics from an Equivalence Principle
• A Statistical Interpretation of Space and Classical-Quantum duality
• Quantum Transformations
• The Equivalence Principle of Quantum Mechanics: Uniqueness Theorem
• Infrared and ultraviolet cutoffs of quantum field theory
• Equivalence Principle: Tunnelling, Quantized Spectra and Trajectories from the Quantum HJ Equation
• Equivalence Principle, Planck Length and Quantum Hamilton-Jacobi Equation
• Equivalence Postulate and Quantum Origin of Gravitation
• Volume average regularization for the Wheeler-DeWitt equation
• Inconstant Planck's constant
• Analysis of the Wheeler-DeWitt Equation beyond Planck Scale and Dimensional Reduction
• Classical Limit of the Trajectory Representation of Quantum Mechanics, Loss of Information and Residual Indeterminacy
• A Class of Exact Solutions of the Wheeler -- De Witt Equation
• Which causality? Differences between the trajectory and Copenhagen analyses of an impulsive perturbation
• Strong Coupling Quantum Gravity and Physics beyond the Planck Scale
• Energy Quantisation and Time Parameterisation

Cited by in corpus (7)

• Proper time reparametrization in cosmology: Mobius symmetry and Kodama charges
• Lorentzian wormholes supported by tachyon matter
• Emergent gravity at all scales
• A Mechanism for Dark Matter and Dark Energy in the Theory of Causal Fermion Systems
• Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• Spinor-Vector Duality and the Swampland
• Universe as Klein-Gordon Eigenstates