Quantum-Gravity Stochastic Effects on the de Sitter Event Horizon

Abstract

The stochastic character of the cosmological constant arising from the non-linear quantum-vacuum Bohm interaction in the framework of the manifestly-covariant theory of quantum gravity (CQG theory) is pointed out. This feature is shown to be consistent with the axiomatic formulation of quantum gravity based on the hydrodynamic representation of the same CQG theory developed recently. The conclusion follows by investigating the indeterminacy properties of the probability density function and its representation associated with the quantum gravity state, which corresponds to a hydrodynamic continuity equation that satisfies the unitarity principle. As a result, the corresponding form of stochastic quantum-modified Einstein field equations is obtained and shown to admit a stochastic cosmological de Sitter solution for the space-time metric tensor. The analytical calculation of the stochastic averages of relevant physical observables is obtained. These include in particular the radius of the de Sitter sphere fixing the location of the event horizon and the expression of the Hawking temperature associated with the related particle tunneling effect. Theoretical implications for cosmology and field theories are pointed out.

The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity

“…Despite its apparent simplicity, Equation ( 23 ) is of paramount importance. In fact, as discussed elsewhere in detail [ 7 , 8 , 12 ], besides the quantum wave function the same equation actually prescribes uniquely also the evolution of the background metric tensor which determines the geometry of space-time.…”

“…A crucial property of such a classical Hamiltonian structure underlying EFE is that of being constraint-free and manifestly covariant when expressed in suitable superabundant canonical variables. The above quantization is unitary in character because the effect of possible quantum sources and sinks (leading respectively to creation and destruction of massive gravitons) is expected to be highly localized, as these events should presumably occur very close to black hole event horizons [ 11 , 12 ]. Therefore, for this reason they can be safely neglected at least in first formulation of the theory.…”

Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity

“…We further notice that different realizations of Equation ( 14) could be distinguished, depending on the functional form of the half-width parameter ε, according to the discussion reported in reference [31]. However, for the scope of the present work and without limitations, in the following, we shall adopt the framework corresponding to assuming ε = const.…”

The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

“…For this reason in this paper the so-called manifestly covariant approach to QG (CQG-theory) recently developed in Refs. [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ] will be adopted.…”

“…This provides a promising and innovative theoretical framework that should be regarded as a plausible route (to QG) in view of the axiomatically self-consistent, perspicuous and mathematically-tractable formalism as well as a number of conceptual new features of CQG-theory that depart it in several ways from previous literature. This conclusion is supported by the theoretical outcomes established so far by CQG-theory and the remarkable number of analytical results, experimentally-testable predictions and even basic conceptual innovations achieved so far in such a framework, which concern, for example, the existence of an invariant discrete-energy spectrum for the quantum gravitational field [ 20 ] and the consequent graviton mass estimate, the emergent gravity picture related to the generalized-Lagrangian path representation of CQG-theory [ 22 ], the novel quantum-gravity interpretation of the cosmological constant as arising due to the Bohm vacuum graviton self-interaction [ 23 , 25 , 26 ], the non-unitary generalization of CQG-theory due to graviton sinks/sources [ 24 ], the quantum screening effect of the cosmological constant [ 25 ], the discovery of the stochastic nature of the deSitter event horizon [ 26 ], the validity of generalized Heisenberg inequalities expressed in 4-tensor form [ 21 ], particularly in connection with the discovery of the proper time-conjugate canonical momentum Heisenberg inequality and the related new statistical interpretation of the concept of invariant minimal length arising in the context of QG [ 27 ].…”