Related papers: Quantum relativistic cosmology: dynamical interpre…
We present perfect fluid Friedmann-Robertson-Walker quantum cosmological models in the presence of negative cosmological constant. In this work the Schutz's variational formalism is applied for radiation, dust, cosmic string, and domain…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative…
Loop quantum cosmology of the k=0 FRW model (with a massless scalar field) is shown to be exactly soluble if the scalar field is used as the internal time already in the classical Hamiltonian theory. Analytical methods are then used i) to…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an…
The cosmological scale factor $a(t)$ of the flat-space Robertson-Walker geometry is examined from a Hamiltonian perspective wherein $a(t)$ is interpreted as an independent dynamical coordinate and the curvature density $\sqrt {- g(a)}…
Wheeler-Dewitt equation for the wave function of the universe appeared long ago in an approach to quantization of gravity. Presently, the universe considered as the microuniverse, very tiny universe compared to the outer universe to which…
First a Friedmann-Robertson-Walker (FRW) universe filled with dust and a conformally invariant scalar field is quantized. For the closed model we find a discrete set of wormhole quantum states. In the case of flat spacelike sections we find…
In the present work, we discuss the Wheeler-DeWitt quantization scheme for an n-dimensional anisotropic cosmological model with a perfect fluid in presence of a massless scalar field. We identify the time parameter using the generalization…
We specify the semiclassical no-boundary wave function of the universe without relying on a functional integral of any kind. The wave function is given as a sum of specific saddle points of the dynamical theory that satisfy conditions of…
In this article we perform the Wheeler-DeWitt quantization for Bianchi type $I$ anisotropic cosmological model in the presence of a scalar field minimally coupled to the Einstein-Hilbert gravity theory. We also consider the cosmological…
In the minisuperspace models of quantum cosmology, the absence of time in the Wheeler-DeWitt (constraint) equation, is the main point leading to the generally accepted conclusion that in the quantum cosmology there is no possibility to…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
The development of last years in quantum geometrodynamics highlights new problems which were not obvious in its first formulation proposed by Wheeler and DeWitt. At the first stage the main task was to apply known quantization schemes to…
We employ Riesz's fractional derivative into the Wheeler--DeWitt equation for a closed de Sitter geometry and obtain the no-boundary and tunneling wavefunctions. From the corresponding probability distributions, the event horizon of the…
In this contribution we sketch a branch-cut quantum formulation of the Wheeler-DeWitt equation analytically continued to the complex plane. As a starting point, we base our approach on the Ho\v{r}ava-Lifshitz formulation of gravity, which…
We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced…
The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with…
It is generally believed that one cannot obtain a large Universe from quantum cosmological models without an inflationary phase in the classical expanding era because the typical size of the Universe after leaving the quantum regime should…