The geometrical origin of dark energy

Faraggi, Alon E ORCID: 0000-0001-7123-6414 and Matone, Marco (2020) The geometrical origin of dark energy. EUROPEAN PHYSICAL JOURNAL C, 80 (11). 11-.

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Official URL: http://dx.doi.org/10.1140/epjc/s10052-020-08665-6

Abstract

The geometrical formulation of the quantum Hamilton-Jacobi theory shows that the quantum potential is never trivial, so that it plays the r\^ole 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 Weizs\"acker 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.

Item Type:	Article
Additional Information:	Comments and references added. Typos corrected. 20 pages
Uncontrolled Keywords:	hep-th, hep-th, astro-ph.CO, gr-qc, hep-ph, quant-ph
Depositing User:	Symplectic Admin
Date Deposited:	08 Jan 2021 14:57
Last Modified:	18 Jan 2023 23:04
DOI:	10.1140/epjc/s10052-020-08665-6
Open Access URL:	https://link.springer.com/article/10.1140/epjc/s10...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3112944