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

Abstract

Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic equations yielding, in turn, quantum modifications of the Einstein field equations. It is shown that in the case of the DeSitter space–time sequences of small-size periodic perturbations with prescribed frequency are actually permitted, each one with its characteristic initial phase. The same perturbations give rise to non-linear modifications of the Einstein field equations in terms of a suitable stochastic-averaged and divergence-free quantum stress-energy tensor. As a result, a quantum-driven screening effect arises which is shown to affect the magnitude of the cosmological constant. Observable features on the DeSitter space–time solution and on the graviton mass estimate are pointed out.

Classical Variational Theory of the Cosmological Constant and Its Consistency with Quantum Prescription

“…The implication is therefore that Λ 1 (s) can actually be identified with Λ CQG (s), acquiring therefore a well-defined quantum prescription. Finally, it must be stressed that the same conclusions apply also in the more general case in which the CGQ-cosmological constant is subject to the additional quantum-driven screening mechanism pointed out in [76], which can affect the absolute magnitude of the CC but not its functional dependence established by Equation (42).…”

Quantum-Gravity Stochastic Effects on the de Sitter Event Horizon

“…More precisely, the emphasis here is its connection with the so-called quantum-modified Einstein field equations (EFE), which determine the continuum background metric tensor . As pointed out earlier in [ 49 , 50 ] in the framework of CQG theory, its construction is based on suitable rigorous, but also physically-intuitive considerations. For convenience, especially in view of the stochastic generalization of the CQG theory to be later discussed in Section 3 , the content is organized into the following subsections: Section 2.1 : GLP representation of CQG theory.…”

“…The first one was referred to as the first-type emergent gravity paradigm and consists of the fact that CQG theory preserves the functional form of the Einstein equations while generating self-consistent quantum corrections to the same field equations obtained without introducing the semiclassical limit. In fact, the canonical theory has permitted the explicit construction of non-perturbative quantum-modified Einstein field equations (EFE) [ 49 , 50 ], which can be derived from the quantum Hamiltonian equations by imposing suitable initial conditions on the hydrodynamic state evaluated at initial proper-time . The remarkable feature is that in both cases considered in [ 49 , 50 ] for different initial conditions of , the resulting quantum-modified EFE carry a non-vanishing stress-energy tensor associated with a quantum cosmological constant, which warrants the existence of a cosmological de Sitter solution for the corresponding quantum-modified background metric tensor (see also the mathematical details below in Section 2 ).…”

“…In fact, the canonical theory has permitted the explicit construction of non-perturbative quantum-modified Einstein field equations (EFE) [ 49 , 50 ], which can be derived from the quantum Hamiltonian equations by imposing suitable initial conditions on the hydrodynamic state evaluated at initial proper-time . The remarkable feature is that in both cases considered in [ 49 , 50 ] for different initial conditions of , the resulting quantum-modified EFE carry a non-vanishing stress-energy tensor associated with a quantum cosmological constant, which warrants the existence of a cosmological de Sitter solution for the corresponding quantum-modified background metric tensor (see also the mathematical details below in Section 2 ). The second feature, denoted as the second-type emergent gravity paradigm, refers instead to the possibility of prescribing the deterministic background metric tensor by means of a suitably-defined quantum/stochastic expectation value of the quantum state.…”

“…Based on these premises, in the present research, we intend to address the theoretical problem of investigating stochastic phenomena induced by quantum gravity effects in the framework of CQG theory, which can characterize, in particular, physical observables of the cosmological de Sitter solution. Starting from the treatment initiated in [ 47 , 49 , 50 , 51 ], the issue pertains first to the determination of the stochastic character of the cosmological constant arising from the non-linear quantum-vacuum Bohm interaction as predicted by CQG theory. This feature follows by investigating the quantum hydrodynamic equations characteristic of CQG theory.…”