Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

Abstract

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestlycovariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant propertime parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time

“…The establishment of features that might affect the large-scale behavior of classical solutions of the same EFE expressed in terms of the structure of background space-time has been a subject of increasing interest in the scientific community (e.g., see Refs. [7][8][9][10][11]). In fact, over the past fifty years, a plethora of disparate approaches and theories have been devoted to quantum gravity.…”

“…The CQG-theory implies, in particular, the validity of 4−tensor quantum Hamilton equations, to be intended as quantum hydrodynamic equations associated with the quantum wave function ψ, and prescribed in terms of a Hamiltonian hydrodynamic state x = g µν , Π µν , where g µν and Π µν denote independent 4−tensor canonical variables identified respectively with the generalized Lagrangian coordinates and conjugate canonical momenta. The latter canonical theory has permitted the explicit construction of non-perturbative quantum-modified EFE [7,36], identified with a suitable stationary form of the quantum Hamiltonian equations obtained by imposing suitable "equilibrium" initial conditions to the Hamiltonian hydrodynamic state, characterized by having vanishing canonical momentum. This made possible also a novel quantum prescription of the cosmological constant (CC), generated by the non-linear Bohm potential associated with the gravitational field quantum-vacuum self-interaction occurring among massive gravitons.…”

Hamilton–Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity

“…The approach is extended here to the more general and physically-significant case of a non-stationary setting of the form g µν = g µν (r, s) ≡ g µν (s) (see Refs. [22,24]). The Hamiltonian theory is found to be represented by the classical Hamiltonian structure {x, H} , which is formed by an appropriate extended 4-tensor canonical state x ≡ g µν , Π α µν and a suitable 4−scalar Hamiltonian density H (x, x(s), r, s) , where g µν represents the Lagrangian coordinate expressed by the second-order variational field 4-tensor of the gravitational field and Π α µν is its conjugate third-order momentum 4-tensor.…”

“…This conclusion provides a theoretical support to the quantum gravity theory early developed in Refs. [19][20][21][22]24], proving that the description of massive quantum gravitons is indeed a characteristic feature of the manifestly-covariant theory and a strict consequence of its formalism. The present outcome also gives completeness to the canonical formalism of the theory and reinforces the strong symmetry link existing between the continuum classical canonical framework and the corresponding discrete quantum representation of the theory of gravitational field.…”

“…The symmetry properties of space-time related to the emergent gravity phenomenon, whereby certain physical observables/characteristics of classical General Relativity follow from quantum gravity theory. These concern both the prescription of the local-coordinate value of the space-time metric tensor, via a suitable quantum expectation value, as well as the establishment of the very functional form of the General Relativity field equations [22,24].…”