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

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

Tunneling probability for the birth of an universe with radiation in Horava-Lifshitz theory

In the present work, we study the birth of a homogeneous and isotropic Friedmann Lemaitre Robertson Walker (FLRW) cosmological model, considering Horava Lifshitz (HL) as the gravitational theory. The matter content of the model is a radiation perfect fluid. In order to study the birth of the universe in the present model, we consider the quantum cosmology mechanism of creation from nothing. In that mechanism, the universe appears after the wavefunction associated to that universe tunnels through a potential barrier. We started studying the classical model. We draw the phase portrait of the model and identify qualitatively all types of dynamical behaviors associated to it. Then, we write the Hamiltonian of the model and apply the Dirac quantization procedure to quantize a constrained theory. We find the appropriate Wheeler-DeWitt equation and solve it using the Wentzel Kramers Brillouin (WKB) approximation. Using the WKB solution, to the Wheeler DeWitt equation, we compute the tunneling probabilities for the birth of that universe (TPWKB). Since the WKB wavefunction depends on the radiation energy (E) and the free parameters coming from the HL theory (gc, gr, gs, gLambda), we compute the behavior of TPWKB as a function of E and all the HL parameters gc, gr, gs, gLambda.Comment: The paper has 20 pages and 9 figure