Related papers: Two-Component Formulation of the Wheeler-DeWitt Eq…
The paper addresses the quantization of minisuperspace cosmological models, with application to the Taub Model. By desparametrizing the model with an extrinsic time, a formalism is developed in order to define a conserved Schr\"{o}dinger…
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)…
Exact solutions of the Wheeler-DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schr\"odinger wavefunctionals having support on 3-metrics of constant spatial…
I present the factorization(s) of the Wheeler-DeWitt equation for vacuum FRW minisuperspace universes of arbitrary Hartle-Hawking factor ordering, including the so-called strictly isospectral supersymmetric method. By the latter means, one…
We can obtain one solution of the Hamiltonian constraint equation in the local sense. The form of the state is suggested from the up-to-down method in our previous work. The up-to-down method works for different way in treating the general…
We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such…
Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of…
The Wheeler-DeWitt equation in quantum gravity is timeless in character. In order to discuss quantum to classical transition of the universe, one uses a time prescription in quantum gravity to obtain a time contained description starting…
A quantum cosmological model with radiation and a dilaton scalar field is analysed. The Wheeler-deWitt equation in the mini-superspace induces a Schr\"odinger equation, which can be solved. An explicit wavepacket is constructed for a…
We study the asymptotics of the Schr\"odinger equation with time-dependent potential in dimension one. Assuming that the potential decays sufficiently rapidly as $|x| \to \infty$, we prove that the solution can be written as the sum of a…
We perform a minisuperspace analysis of an information-theoretic nonlinear Wheeler-deWitt (WDW) equation for de Sitter universes. The nonlinear WDW equation, which is in the form of a difference-differential equation, is transformed into a…
We investigate the Wheeler-DeWitt equation for a flat, homogeneous, and isotropic Universe containing a canonical scalar field with a potential. We show that under the constraint $|\Psi|=1$, where the Wheeler-DeWitt equation exactly becomes…
We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do…
We discuss minisuperspace aspects a non empty Robertson-Walker universe containing scalar matter field. The requirement that the Wheeler-DeWitt (WDW) operator be self adjoint is a key ingredient in constructing the physical Hilbert space…
We study approximate solutions of the Wheeler DeWitt (WdW) equation and compare them with the standard results of cosmological perturbation theory. In mini-superspace, we introduce a dimensionless gravitational coupling $\alpha$ that is…
We analyze the Wheeler-DeWitt (WDW) equation in the context of a gravitational collapse. The physics of an expanding/collapsing universe and many details of a collapsing star can classically be described by the Roberston-Walker metric in…
Using the semi-classical approximation to the Wheeler-DeWitt equation obtained via Arnowitt-Deser-Misner (ADM) formalism in the Friedmann-Lemaitre-Robertson-Walker (FLRW) model coupled to a scalar field and positive cosmological constant,…
The present work deals with quantum cosmology for non-minimally coupled scalar field in the background of FLRW space--time model. The Wheeler-DeWitt equation is constructed and symmetry analysis is carried out. The Lie point symmetries are…
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant…
The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wavefunction solutions is such that a…