O. Obregón

Noncommutative self-dual gravity

Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved by the vanishing of commutative torsion. Finally, the noncommutative corrections to the action are computed up to second order.

Supersymmetric Bianchi models and the square root of the Wheeler-DeWitt equation

Abstract By solving the full set of quantum constraint equations for the Bianchi-I mini-superspace model in supergravity, it is found that the wave-function depends only on two arbitrary constants. General solutions to the Wheeler-DeWitt equation or to a corresponding Dirac square root equation are not permitted. Possible extensions of this work to Bianchi IX and other Bianchi types are discussed.

Quantum cosmology: the supersymmetric square root

Using N=1 supergravity as the natural square root of gravity, the authors study the quantum cosmology of Bianchi type I cosmological models. This approach gives us a natural interpretation of the components of the state vector of the universe that was lacking in previous work on the square root of quantum cosmology.

Towards Noncommutative Quantum Black Holes

In this paper we study noncommutative black holes. We use a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate the Hawkings temperature and entropy for the noncommutative Schwarzschild black hole.

Towards a loop representation for quantum canonical supergravity

We study several aspects of the canonical quantization of supergravity in terms of the Ashtekar variables. We cast the theory in terms of a GSU(2) connection and we introduce a loop representation. The solution space is similar to the loop representation of ordinary gravity, the main difference being the form of the Mandelstam identities. Physical states are in general given by knot invariants that are compatible with the GSU(2) Mandelstam identities. There is an explicit solution to all the quantum constraint equations connected with the Chern-Simons form, which coincides exactly with the Dubrovnik version of the Kauffman polynomial. This provides for the first time the possibility of finding explicit analytic expressions for the coefficients of that knot polynomial.

Can primordial wormholes be induced by GUTs at the early Universe

Abstract Using large N, 4d anomaly induced one-loop effective action for conformally invariant matter (typical GUT multiplet) we study the possibility to induce the primordial spherically symmetric wormholes at the early Universe. The corresponding effective equations are obtained in two different coordinate frames. The numerical investigation of these equations is done for matter content corresponding to N =4 SU(N) super Yang-Mills theory. For some choice of initial conditions, the induced wormhole solution with increasing throat radius and increasing red-shift function is found.

INDUCED WORMHOLES DUE TO QUANTUM EFFECTS OF SPHERICALLY REDUCED MATTER IN LARGE N APPROXIMATION

Abstract Using one-loop effective action in large N and s -wave approximation we discuss the possibility to induce primordial wormholes at the early Universe. An analytical solution is found for self-consistent primordial wormhole with constant radius. Numerical study gives the wormhole solution with increasing throat radius and increasing red-shift function. There is also some indication to the possibility of a topological phase transition.

Crossing the phantom divide in an interacting generalized Chaplygin gas

Unified generalized Chaplygin gas models assuming an interaction between dark energy and dark matter fluids have been previously proposed. Following these ideas, we consider a particular relation between dark densities, which allows the possibility of a time varying equation of state for dark energy that crosses the phantom divide at a recent epoch. Moreover, these densities decay throughout the evolution of the Universe, avoiding a big rip. We find also a scaling solution, i.e. these densities are asymptotically proportional in the future, which contributes to the solution of the coincidence problem.Unified generalized Chaplygin gas models assuming an interaction between dark energy and dark matter fluids have been previously proposed. Following these ideas, we consider a particular relation between dark densities, which allows the possibility of a time varying equation of state for dark energy that crosses the phantom divide at a recent epoch. Moreover, these densities decay throughout the evolution of the Universe, avoiding a big rip. We find also a scaling solution, i.e.?these densities are asymptotically proportional in the future, which contributes to the solution of the coincidence problem.

QUANTUM BOUNDS FOR GRAVITATIONAL DE SITTER ENTROPY AND THE CARDY–VERLINDE FORMULA

We analyze different types of quantum corrections to the Cardy–Verlinde entropy formula in a Friedmann–Robertson–Walker universe and in an (anti)-de Sitter space. In all cases we show that quantum corrections can be represented by an effective cosmological constant which is then used to redefine the parameters entering the Cardy–Verlinde formula so that it becomes valid also with quantum corrections, a fact that we interpret as a further indication of its universality. A proposed relation between Cardy–Verlinde formula and the ADM Hamiltonian constraint is given.

Gauge theory of the de Sitter group and the Ashtekar formulation.

A new gauge theory of gravity is introduced. By identifying the gravitational gauge field components with the connection and the metric, the action can be reduced to the gauge theory proposed by MacDowell and Mansouri in addition to the Pontrjagin topological term and, on the other hand, to the Ashtekar action with a cosmological term in addition to the Euler and the Pontrjagin topological terms. The action of the theory is closely related to the Chern-Simons action and is quadratic in the field strength components