Related papers: A cosmological viewpoint on the correspondence bet…
We explore the introduction of the cosmological constant via equivalent transformations in cosmology. We consider the Wheeler-DeWitt equation for the CDM universe and we construct the Hamilton-Jacobi action for the $\Lambda$CDM model. We…
In the case of a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker universe in $f\left( R\right) $-gravity we write the Wheeler-DeWitt equation of quantum cosmology. The equation depends on the functional form of $f\left( R\right)…
We develop a general canonical quantization scheme for $k$-essence cosmology in scalar-tensor theory. Utilizing the Dirac-Bergmann algorithm, we construct the Hamiltonian associated with the cosmological field equations and identify the…
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…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…
In this paper, using a significantly improved version of the model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ, 614, 1), we address an important question: Was there a decelerating past for the universe? To answer…
We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries…
A crucial problem in quantum cosmology is a careful analysis of the one-loop semiclassical approximation for the wave function of the universe, after an appropriate choice of mixed boundary conditions. The results for Euclidean quantum…
It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the…
The deformation theory of curves is studied by using the canonical ideal. The problem of lifting curves with automorphisms is reduced to a lifting problem of linear representations.
A certain approach to solving the Wheeler-DeWitt equation in quantum cosmology, which is based on a type of super-selection rule by which negative frequency solutions are discarded, is discussed. In a preliminary analysis, we recall well…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
The paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since General Relativity does not have a privileged time variable…
We explore at phenomenological level a model of the Universe filled with various kinds of matter characterized by different equations of state. We show that introducing of each kind of matter is equivalent to a certain choice of a gauge…
The prerequisites of the extended phase space approach to quantization of gravity, which is alternative to the Wheeler-DeWitt one and other existing approaches, are presented. The features of the proposed approach and conclusions from its…
Deformation quantization is applied to quantize gravitational systems coupled with matter. This quantization procedure is performed explicitly for quantum cosmology of these systems in a flat minisuper(phase)space. The procedure is employed…
The Wheeler-DeWitt equation is solved for some scalar-tensor theories of gravitation in the case of homogeneous and isotropic cosmological models.We present general solutions corresponding to cosmological term: (i)\lambda(\phi)=0$ and $(ii)…
We revisit the issue of continuous signature transition from Euclidean to Lorentzian metrics in a cosmological model described by FRW metric minimally coupled with a self interacting massive scalar field. Then, using a noncommutative phase…