Theoretical Derivation of the Cosmological Constant in the Framework of the Hydrodynamic Model of Quantum Gravity: Can the Quantum Vacuum Singularity Be Overcome?

Abstract

Abstract:In the present work, it is shown that the problem of the cosmological constant (CC) is practically the consequence of the inadequacy of general relativity to take into account the quantum property of the space. The equations show that the cosmological constant naturally emerges in the hydrodynamic formulation of quantum gravity and that it does not appear in the classical limit because the quantum energy-impulse tensor gives an equal contribution with opposite sign. The work shows that a very large local value of the CC comes from the space where the mass of a quasi-punctual particle is present but that it can be as small as measured on cosmological scale. The theory shows that the small dependence of the CC from the mean mass density of the universe is due to the null contribution coming from the empty space. This fact gives some hints for the explanation of the conundrum of the cosmic coincidence by making a high CC value of the initial instant of universe compatible with the very small one of the present era.

The Hydrodynamic Representation of the Klein-Gordon Equation with Self- Interacting Field

“…is solved as a function of the two real variables, | |ψ and S [2][3][4][5]. As shown by Weiner et al [6], the outputs of the quantum hydrodynamic model agree with the outputs of the Schrödinger problem and, more recently, as shown by Koide and Kodama [7], it agrees with the outputs of the stochastic variational method.…”

“…The biunique correspondence between the standard quantum mechanics and the hydrodynamic representation [1][2][3][4][5][6]17] warrants that the quantum energy-impulse tensor density can be independently defined by the used formalism.…”

The CPT-RICCI Scalar Curvature Symmetry in Quantum Electro-Gravity

“…As shown by Bialiniki-Birula et al and by the author himself [14,22], it is noteworthy to observe that, due to the biunique relation between the quantum hydrodynamic equations (2.a-2.b) and the quantum equation (1), equations (23)(24) are equivalent to the Klein-Gordon one…”

“…Moreover, eq. (35-36) shows the presence of the cosmological constant that, due to the quantum potential derivatives, is different from zero just in the places where the mass is localized (in quasi-punctual particles) so that the spatial mean can lead to the right order of magnitude of the cosmologically observed values [23].…”

The Non-Euclidean Hydrodynamic Klein–Gordon Equation with Perturbative Self-Interacting Field

“…as a function of the two real variables, | | and S [60,62,63,[69][70][71][72][73]. The model gives rise to classical-like analogy describing the motion of particles' density…”