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

Nonminimal Scalar-Tensor Theories and Quantum Gravity

Recentely, it is shown that the quantum effects of matter determine the conformal degree of freedom of the space-time metric. This was done in the framework of a scalar-tensor theory with one scalar field. A point with that theory is that the form of quantum potential is preassumed. Here we present a scalar-tensor theory with two scalar fields, and no assumption on the form of quantum potential. It is shown that using the equations of motion one gets the correct form of quantum potential plus some corrections.Comment: 15 page

About Some Problems Raised by the Relativistic Form of De-Broglie--Bohm Theory of Pilot Wave

The standard relativistic de-Broglie--Bohm theory has the problems of tacyonic solutions and the incorrect non-relativistic limit. In this paper we obtain a relativistic theory, not decomposing the relativistic wave equations but looking for a generalization of non-relativistic Bohmian theory in such a way that the correct non-relativistic limit emerges. In this way we are able to construct a relativistic de-Broglie--Bohm theory both for a single particle and for a many-particle system. At the end, the theory is extended to the curved space-time and the connection with quantum gravity is discussed.Comment: 13 pages, RevTeX. To appear in Physica Scripta, 200

On the effect of renormalization group improvement on the cosmological power spectrum

Asymptotically safe quantum gravity predicts running gravitational and cosmological constants, while it remains a meaningful quantum field theory because of the existence of non-Gaussian ultraviolet fixed points. Here we have investigated the effect of such running couplings on the cosmological perturbations. We have obtained the improved Mukhanov-Sassaki equation and solved it for two models. The effect of asymptotically safe quantum gravity on the cosmological power spectrum is also studied

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

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