M. Sabido

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.

Noncommutative topological theories of gravity

The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a

Towards Noncommutative Quantum Black Holes

SL(2,\mathbf{C})

S duality in (2+1)-dimensional Chern-Simons supergravity

complex connection, from which the Euler characteristic and the signature invariant are obtained. Finally, we speculate on the description of noncommutative gravitational instantons, as well as noncommutative local gravitational anomalies.

On noncommutative minisuperspace and the Friedmann equations

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.

Effects of deformed phase space on scalar field cosmology

Strong/weak coupling duality in Chern-Simons supergravity is studied. It is argued that this duality can be regarded as an example of superduality. The use of supergroup techniques for the description of Chern-Simons supergravity greatly facilitates the analysis.

Noncommutativity and scalar field cosmology

Abstract In this Letter we present a noncommutative version of scalar field cosmology. We find the noncommutative Friedmann equations as well as the noncommutative Klein–Gordon equation, interestingly the noncommutative contributions are only present up to second order in the noncommutative parameter. Finally we conclude that if we want a noncommutative minisuperspace with a constant noncommutative parameter as viable phenomenological model, the noncommutative parameter has to be very small.

Scalar potentials out of canonical quantum cosmology

The effects of phase space deformations in standard scalar field cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables to have a deformed Poisson algebra among the coordinates and the canonical momenta. It is found that in the deformed minisuperspace model the volume of the universe is non singular. Finally, the late time evolution gives rise to an accelerating scale factor, this acceleration is a consequence of the noncommutative deformation.

Deformed phase space Kaluza–Klein cosmology and late time acceleration

In this work we extend and apply a previous proposal to study noncommutative cosmology to the Friedmann-Robertson-Walker cosmological background coupled to a scalar field. This is done in classical and quantum scenarios. In both cases noncommutativity is introduced in the gravitational field as well as in the scalar field through a deformation of minisuperspace, and we are able to find exact solutions. Finally, the effects of noncommutativity on the classical evolution are analyzed.

Noncommutative Bianchi Type II Quantum Cosmology

Using canonical quantization of a flat FRW cosmological model containing a real scalar field ϕ endowed with a scalar potential V(ϕ), we are able to obtain exact and semi-classical solutions of the so-called Wheeler–DeWitt equation for a particular family of scalar potentials. Some features of the solutions and their classical limits are discussed.