Related papers: Non-Riemannian model of the space-time responsible…
Several other factors, besides the intrinsic local geometry, contribute to give a meaning to a space-time model. The simplest example comes from comparing Minkowski's and Milne's model, that both have a null Riemann tensor. We add to these…
We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered…
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature…
Space-time--time is a natural hybrid of Kaluza's five-dimensional geometry and Weyl's conformal space-time geometry. Translations along the secondary time dimension produce the electromagnetic gauge transformations of Kaluza--Klein theory…
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial…
The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial…
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently…
We give the generalization of the method of the space-time description of particle creation by a gravitational field for a scalar field with nonconformal coupling to the curvature. The space-time correlation function is obtained for a…
Quantum effects play an essential role in modern cosmology. Perhaps the most striking example comes from large-scale structures, generally assumed to originate from vacuum quantum fluctuations and stretched by an expansion phase. Inflation…
At present we have only the very successful but phenomenological Einstein geometrical modelling of the spacetime phenomenon. This geometrical model provides a `container' for other theories, in particular the quantum field theories. Here we…
The semiclassical gravity describes gravitational back-reactions of the classical spacetime interacting with quantum matter fields but the quantum effects on the background is formally defined as higher derivative curvatures. These induce…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
This article deals with a nonrelativistic cosmological model based on Galilean covariance, formulated within a five-dimensional Galilean manifold. Within this framework, we construct an isotropic and homogeneous metric analogous to the…
The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…
In the event symmetric approach to quantum gravity it is assumed that the fundamental laws of physics must be invariant under exchange of any two space-time events. The fact that this symmetry if obviously not observed is attributed to the…
A free massless scalar field is coupled to homogeneous and isotropic loop quantum cosmology. The coupled model is investigated in the vicinity of the classical singularity, where discreteness is essential and where the quantum model is…