Abstract:
we argue that the copenhagen interpretation of quantum mechanics cannot be applied to quantum cosmology. among the alternative interpretations, we choose to apply the bohm-de broglie interpretation of quantum mechanics to canonical quantum cosmology. for minisuperspace models, we show that there is no problem of time in this interpretation, and that quantum effects can avoid the initial singularity, create inflation and isotropize the universe. for the general case, it is shown that, irrespective of any regularization or choice of factor ordering of the wheeler-dewitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. the other quantum effects are either trivial or break the four-geometry of spacetime. a bohm-de broglie picture of a quantum geometrodynamics is constructed, which allows the investigation of these latter structures.

Abstract:
We argue that the Copenhagen interpretation of quantum mechanics cannot be applied to quantum cosmology. Among the alternative interpretations, we choose to apply the Bohm-de Broglie interpretation of quantum mechanics to canonical quantum cosmology. For minisuperspace models, we show that there is no problem of time in this interpretation, and that quantum effects can avoid the initial singularity, create inflation and isotropize the Universe. For the general case, it is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of a quantum geometrodynamics is constructed, which allows the investigation of these latter structures.

Abstract:
It is generally believed that one cannot obtain a large Universe from quantum cosmological models without an inflationary phase in the classical expanding era because the typical size of the Universe after leaving the quantum regime should be around the Planck length, and the standard decelerated classical expansion after that is not sufficient to enlarge the Universe in the time available. For instance, in many quantum minisuperspace bouncing models studied in the literature, solutions where the Universe leave the quantum regime in the expanding phase with appropriate size have negligible probability amplitude with respect to solutions leaving this regime around the Planck length. In this paper, I present a general class of moving gaussian solutions of the Wheeler-DeWitt equation where the velocity of the wave in minisuperspace along the scale factor axis, which is the new large parameter introduced in order to circumvent the abovementioned problem, induces a large acceleration around the quantum bounce, forcing the Universe to leave the quantum regime sufficiently big to increase afterwards to the present size, without needing any classical inflationary phase in between, and with reasonable relative probability amplitudes with respect to models leaving the quantum regime around the Planck scale. Furthermore, linear perturbations around this background model are free of any transplanckian problem.

Abstract:
I make a review on the aplications of the Bohm-De Broglie interpretation of quantum mechanics to quantum cosmology. In the framework of minisuperspaces models, I show how quantum cosmological effects in Bohm's view can avoid the initial singularity, isotropize the Universe, and even be a cause for the present observed acceleration of the Universe. In the general case, we enumerate the possible structures of quantum space and time.

Abstract:
It is shown in this paper that minisuperspace quantization of homogeneous and isotropic geometries with phantom scalar fields, when examined in the light of the Bohm-de Broglie interpretation of quantum mechanics, does not eliminate, in general, the classical big rip singularity present in the classical model. For some values of the Hamilton-Jacobi separation constant present in a class of quantum state solutions of the Wheeler-DeWitt equation, the big rip can be either completely eliminated or may still constitute a future attractor for all expanding solutions. This is contrary to the conclusion presented in Ref.[1], using a different interpretation of the wave function, where the big rip singularity is completely eliminated ("smoothed out") through quantization, independently of such separation constant and for all members of the above mentioned class of solutions. This is an example of the very peculiar situation where different interpretations of the same quantum state of a system are predicting different physical facts, instead of just giving different descriptions of the same observable facts: in fact, there is nothing more observable than the fate of the whole Universe.

Abstract:
We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing.

Abstract:
We propose a new cosmological paradigm in which our observed expanding phase is originated from an initially large contracting Universe that subsequently experienced a bounce. This category of models, being geodesically complete, is non-singular and horizon-free, and can be made to prevent any relevant scale to ever have been smaller than the Planck length. In this scenario, one can find new ways to solve the standard cosmological puzzles. One can also obtain scale invariant spectra for both scalar and tensor perturbations: this will be the case, for instance, if the contracting Universe is dust-dominated at the time at which large wavelength perturbations get larger than the curvature scale. We present a particular example based on a dust fluid classically contracting model, where a bounce occurs due to quantum effects, in which these features are explicit.

Abstract:
We study the quantized Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) model minimally coupled to a free massless scalar field. In a previous paper, \cite{fab2}, solutions of this model were constructed as gaussian superpositions of negative and positive modes solutions of the Wheeler-DeWitt equation, and quantum bohmian trajectories were obtained in the framework of the Bohm-de Broglie (BdB) interpretation of quantum cosmology. In the present work, we analyze the quantum bohmian trajectories of a different class of gaussian packets. We are able to show that this new class generates bohmian trajectories which begin classical (with decelerated expansion), undergo an accelerated expansion in the middle of its evolution due to the presence of quantum cosmological effects in this period, and return to its classical decelerated expansion in the far future. We also show that the relation between luminosity distance and redshift in the quantum cosmological model can be made close to the corresponding relation coming from the classical model suplemented by a cosmological constant, for $z<1$. These results suggest the posibility of interpreting the present observations of high redshift supernovae as the manifestation of a quantum cosmological effect.

Abstract:
In this paper it is shown how to obtain the simplest equations for the Mukhanov-Sasaki variables describing quantum linear scalar perturbations in the case of scalar fields without potential term. This was done through the implementation of canonical transformations at the classical level, and unitary transformations at the quantum level, without ever using any classical background equation, and it completes the simplification initiated in investigations by Langlois \cite{langlois}, and Pinho and Pinto-Neto \cite{emanuel2} for this case. These equations were then used to calculate the spectrum index $n_s$ of quantum scalar perturbations of a non-singular inflationary quantum background model, which starts at infinity past from flat space-time with Planckian size spacelike hypersurfaces, and inflates due to a quantum cosmological effect, until it makes an analytical graceful exit from this inflationary epoch to a decelerated classical stiff matter expansion phase. The result is $n_s=3$, incompatible with observations.

Abstract:
It is shown in this letter that in the framework of an inhomogeneous geometry and a massive non self-interacting scalar field with spherical symmetry, one needs a homogeneous patch bigger than a dizaine of horizons in order to start inflation. The results are completly independent of initial conditions on the spatial distribution of the scalar field. The initial condition on the metric parameters are also justified. This is a generalization of the results obtained in Ref.[1], showing that their conclusions are rather robust.