534 research outputs found
Canonical transformation for stiff matter models in quantum cosmology
In the present work we consider Friedmann-Robertson-Walker models in the
presence of a stiff matter perfect fluid and a cosmological constant. We write
the superhamiltonian of these models using the Schutz's variational formalism.
We notice that the resulting superhamiltonians have terms that will lead to
factor ordering ambiguities when they are written as operators. In order to
remove these ambiguities, we introduce appropriate coordinate transformations
and prove that these transformations are canonical using the symplectic method.Comment: Revtex4 Class, 3 pages, No Figure
A canonical transformation and the tunneling probability for the birth of an asymptotically DeSitter universe with dust
In the present work, we study the quantum cosmology description of closed
Friedmann-Robertson-Walker models in the presence of a positive cosmological
constant and a generic perfect fluid. We work in the Schutz's variational
formalism. If one uses the scale factor and its canonically conjugated momentum
as the phase space variables that describe the geometrical sector of these
models, one obtains Wheeler-DeWitt equations with operator ordering
ambiguities. In order to avoid those ambiguities and simplify the quantum
treatment of the models, we introduce new phase space variables. We explicitly
demonstrate that the transformation leading from the old set of variables to
the new one is canonical. In order to show that the above canonical
transformations simplify the quantum treatment of those models, we consider a
particular model where the perfect fluid is dust. We solve the Wheeler-DeWitt
equation numerically using the Crank-Nicholson scheme and determine the time
evolution of the initial wave function. Finally, we compare the results for the
present model with the ones for another model where the only difference is the
presence of a radiative perfect fluid, instead of dust.Comment: Revtex4, 18 pages, 2 EPS figure
Reply to "Comment on 'Quantization of FRW spacetimes in the presence of a cosmological constant and radiation'"
The Comment by Amore {\it et al.} [gr-qc/0611029] contains a valid criticism
of the numerical precision of the results reported in a recent paper of ours
[Phys. Rev. D {\bf 73}, 044022 (2006)], as well as fresh ideas on how to
characterize a quantum cosmological singularity. However, we argue that,
contrary to what is suggested in the Comment, the quantum cosmological models
we studied show hardly any sign of singular behavior.Comment: 4 pages, accepted by Physical Review
- âŠ