The Bohm - de Broglie Interpretation in Quantum 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 to 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 contracts to a minimum size and bounce
to an
expansion phase reaching the classical standard time
development. The quantum
potential avoides the singularity, and creates an inflationary
phase. They are models
without particle horizons. These models have as material
sources 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. It was also verified that
quantum
cosmology for homogeneous fields (in the minisuperspace)
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 Sergio Santini, it was
demonstrated that this result is
no more 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.