Related papers: Solving the Wheeler-DeWitt of Small Universe
In the analysis of the Wheeler-DeWitt equation, we have simplified the Hamiltonian constraint of the Wheeler-DeWitt equation using the coordinate transformation. The coordinate is choose such that metric becomes diagonal and as Gaussian…
One of the unsolved issues in the quantum gravity comes from the Wheeler-DeWitt equation, which is second order functional derivative equation. In this paper, we introduce a new method to solve the Wheeler-DeWitt equation. Usually one…
The Wheeler-DeWitt Equation represents a tool to study Quantum Gravity and Quantum Cosmology. Its solution in a very general context is, of course, impossible. To this purpose we consider some distortions of General Relativity like…
In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of…
The central equation of quantum gravity is the Wheeler-DeWitt equation. We give an argument suggesting that exact solutions of this equation give a surface in the space of coupling constants. This provides a mechanism for determining the…
We give an introduction into quantum cosmology with emphasis on its conceptual parts. After a general motivation we review the formalism of canonical quantum gravity on which discussions of quantum cosmology are usually based. We then…
For pure fourth order (${\cal{L}} \propto R^2$) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that $\Psi = 0$ at the origin…
The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor gravitational theory in the case of Friedmann-Robertson- Walker cosmological model. We present solutions for several cosmological functions: i) \lambda(\phi)=0,…
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 $f\left( R\right)…
Wheeler-Dewitt equation for the wave function of the universe appeared long ago in an approach to quantization of gravity. Presently, the universe considered as the microuniverse, very tiny universe compared to the outer universe to which…
The Wheeler-DeWitt equation is solved for some scalar-tensor theories of gravitation in the case of homogeneous and isotropic cosmological models.We present general solutions corresponding to cosmological term: (i)\lambda(\phi)=0$ and $(ii)…
The two dimensional dilaton gravity with the cosmological term and with an even number of matter fields minimally coupled to the gravity is considered. The exact solutions to the Wheeler-DeWitt equation are obtained in an explicit…
The stability of the minisuperspace model of the early universe is studied by solving the Wheeler-DeWitt equation numerically. We consider a system of Einstein gravity with a scalar field. When we solve the Wheeler-DeWitt equation, we pick…
This is a pedagogical paper which explains some ideas in cosmology at a level accessible to undergraduate students. It does not use general relativity, but uses the ideas of Newtonian cosmology worked out by Milne and McCrea. The…
We consider the Wheeler-De Witt equation for canonical quantum gravity coupled to massless scalar field. After regularizing and renormalizing this equation, we find a one-parameter class of its solutions.
The Wheeler -- DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature the opinion that the Wheeler -- DeWitt equation is even more…
Quantum cosmology is studied within the framework of the minimal quantum gravity theory proposed by Ho\v{r}ava. For this purpose we choose the Kantowski-Sachs (KS) model and construct the corresponding Wheeler-DeWitt equation. We study the…
In this paper we present the Wheeler-DeWitt equation of $f(R,L_m)$ gravity in flat FRW universe, which is the first step of the study of quantum $f(R,L_m)$ cosmology. In the minisuperspace spanned by the FRW scale factor $a$ and the Ricci…
We describe a new geometrical solution to the Wheeler-DeWitt equation in two dimensional quantum gravity. The solution is the amplitude of a surface whose boundary consists of two tangent loops. We further discuss a new method for…
One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to…