Effects of Quantum Metric Fluctuations on the Cosmological Evolution in Friedmann-Lemaitre-Robertson-Walker Geometries

Abstract

In this paper, the effects of the quantum metric fluctuations on the background cosmological dynamics of the universe are considered. To describe the quantum effects, the metric is assumed to be given by the sum of a classical component and a fluctuating component of quantum origin . At the classical level, the Einstein gravitational field equations are equivalent to a modified gravity theory, containing a non-minimal coupling between matter and geometry. The gravitational dynamics is determined by the expectation value of the fluctuating quantum correction term, which can be expressed in terms of an arbitrary tensor Kμν. To fix the functional form of the fluctuation tensor, the Newtonian limit of the theory is considered, from which the generalized Poisson equation is derived. The compatibility of the Newtonian limit with the Solar System tests allows us to fix the form of Kμν. Using these observationally consistent forms of Kμν, the generalized Friedmann equations are obtained in the presence of quantum fluctuations of the metric for the case of a flat homogeneous and isotropic geometry. The corresponding cosmological models are analyzed using both analytical and numerical method. One finds that a large variety of cosmological models can be formulated. Depending on the numerical values of the model parameters, both accelerating and decelerating behaviors can be obtained. The obtained results are compared with the standard ΛCDM (Λ Cold Dark Matter) model.

Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

“…However, the concept for gravitational background states in general relativity (GR) is highly problematic because classical GR is a non-linear but otherwise background-independent theory [9]. Nevertheless, vacuum energy and dark energy may contribute to potential gravitational background states and to the expansion of the universe through the cosmological constant Λ [26]. So far, the calculations on the contributions to Λ by different sources do not provide a satisfactory explanation to its small positive value [27].…”

Covariant Space-Time Line Elements in the Friedmann-Lemaitre-Robertson-Walker Geometry

“…It has to be remarked that this mathematical constraint does not truly constitute a quantum gravity theory per se. It relies on specific solutions to classical GR equations, without coupling an external mass field, unlike semi-classical formulations of quantum gravity [22]. Explicit quantization of space-time is not introduced as well.…”

“…As the space-time metric in GR is shaped by energy-momentum densities through the energy-momentum tensor, vacuum energy and momentum fluctuations from the uncertainty principle should perturb the space-time [19,22]. Indeed, very early on it was assumed that in the context of a quantum description of gravity, quantum fluctuations caused by Heisenberg´s principle play a major role [23].…”

Covariant Space-Time Line Elements in the Friedmann-Lemaitre-Robertson-Walker Geometry

“…Independently of the specific model for quantum gravity, uncertainty fluctuations introduce a perturbation in the metric that is unrelated to classical gravitation, but can be otherwise related to a minimal length for the space-time line element [19,22,[25][26][27]. However, the use of a fixed length for the line element clashes with classical relativity.…”