3.a The Bohm - de Broglie Interpretation in Cosmology

This is an alternative interpretation to the Copenhaguen interpretation of quantum mechanics that can be used in quantum cosmology. In this interpretation there is no need for a division of the world in quantum and classical because it is an ontological theory of matter: the actual facts are there ab initio. The quantum effects are generated by a new non-local quantum potential that appears naturally from the Schrödinger equation (or from the Wheeler-DeWitt equation in quantum cosmology).

Concerning minisuperspace models, in the papers by Nelson Pinto Neto, José Acácio de Barros, Júlio César Fabris, Roberto Colistete Jr., Alexandre da Fonseca Velasco e Marco Antonio Sagioro-Leal, it was verified the existence of quantum cosmological models without singularities which contract to a minimum size and bounce to an expansive phase, reaching later the standard time development in the classical regime. The quantum potential avoids the singularity, and creates an inflationary phase. These models do not have particle horizons, and their material sources are either radiation or a free scalar field. We are now studying the evolution of cosmological perturbations in these scenarios, and the consequences of the existence of such quantum bounces over the anisotropies in the CMBR. We are also generalizing these results to more elaborated matter sources and more general initial conditions for the cosmological wave function.

It was also verified that the quantum potential can generate isotropic phases in anisotropic cosmological models, and as such it can be an alternative mechanism to inflation to isotropize the Universe.

We were able to show that quantum cosmology for homogeneous fields (in the minisuperspace approach) following this interpretation does not present ambiguities in the choice of the variable which will play the role of time: all choices yield the same physical result. However, in a paper by Nelson Pinto Neto and Eduardo Sérgio Santini, it was demonstrated that this result is not valid for general inhomogeneous models (the full superspace), e.g., the existence of the quantum potential breaks the fundamental symmetries of classical General Relativity, the unity of spacetime, generating principal directions. The symmetry group of these spacetimes is no longer the diffeomorphism group but a more restricted group. We are investigating these new symmetry groups in detail.