Quantum Einstein's Equations and Constraints Algebra

In this paper we shall address this problem: Is quantum gravity constraints algebra closed and what are the quantum Einstein equations. We shall investigate this problem in the de-Broglie--Bohm quantum theory framework. It is shown that the constraint algebra is weakly closed and the quantum Einstein's equations are derived.Comment: 13 pages, No figure, RevTeX. To appear in Pramana J. Phys., 200

Regularizing future cosmological singularities with varying speed of light

Cosmological models may result in future singularities. We show that, in the framework of dynamical varying speed of light theories, it is possible to regularize those singularities

Causal loop quantum cosmology in momentum space

We shall show that it is possible to make a causal interpretation of loop quantum cosmology using the momentum as the dynamical variable. We shall show that one can derive Bohmian trajectories. For a sample cosmological solution with cosmological constant, the trajectory is plotted.Comment: 21 pages, 2 figures. To appear in Int. J. Mod. Phys. D, 200

Variational Methods in Loop Quantum Cosmology

An action functional for the loop quantum cosmology difference equation is presented. It is shown that by guessing the general form of the solution and optimizing the action functional with respect to the parameters in the guessed solution one can obtain approximate solutions which are reasonably good.Comment: To appear in EuroPhysics Letter

On the classification of consistent boundary conditions for f(R) \mathit{f}(\mathit{R})-Gravity

Using a completely covariant approach, we discuss the role of boundary conditions (BCs) and the corresponding Gibbons--Hawking--York (GHY) terms in $\mathit{f}(\mathit{R})$-gravity in arbitrary dimensions. We show that $f(\mathit{R})$-gravity, as a higher derivative theory, is not described by a degenerate Lagrangian, in its original form. Hence, without introducing additional variables, one can not obtain consistent BCs, even by adding the GHY terms (except for $f(\mathit{R})=R$). However, following the Ostrogradsky approach, we can introduce a scalar field in the framework of Brans-Dicke formalism to the system to have consistent BCs by considering appropriate GHY terms. In addition to the Dirichlet BC, the GHY terms for both Neumann and two types of mixed BCs are derived. We show the remarkable result that the $f(\mathit{R})$-gravity is itself compatible with one type of mixed BCs, in $D$ dimension, i.e. it doesn't require any GHY term. For each BC, we rewrite the GHY term in terms of Arnowit-Deser-Misner (ADM) variables.Comment: 21 page

Causal Loop Quantum Gravity and Cosmological Solutions

We shall present here the causal interpretation of canonical quantum gravity in terms of new variables. Then we shall apply it to the minisuperspace of cosmology. A vacuum solution of quantum cosmology is obtained and the Bohmian trajectory is investigated. At the end a coherent state with matter is considered in the cosmological model.Comment: 22 pages, 6 figure