Gravitational wave background in perfect fluid quantum cosmologies

We discuss the gravitational wave background produced by bouncing models based on a full quantum evolution of a universe filled with a perfect fluid. Using an ontological interpretation for the background wave function allows us to solve the mode equations for the tensorial perturbations, and we find the spectral index as a function of the fluid equation of state.Comment: 12 pages, 5 figures, to appear in Phys. Rev. D (2006

The Causal Interpretation of Quantum Mechanics and The Singularity Problem in Quantum Cosmology

We apply the causal interpretation of quantum mechanics to homogeneous quantum cosmology and show that the quantum theory is independent of any time-gauge choice and there is no issue of time. We exemplify this result by studying a particular minisuperspace model where the quantum potential driven by a prescribed quantum state prevents the formation of the classical singularity, independently on the choice of the lapse function. This means that the fast-slow-time gauge conjecture is irrelevant within the framework of the causal interpretation of quantum cosmology.Comment: 18 pages, LaTe

Scalar Perturbations in Scalar Field Quantum Cosmology

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.Comment: 10 pages, 2 figures, accepted version to Physical Review D 7

Perturbations in the Ekpyrotic Scenarios

With the new cosmological data gathered over the last few years, the inflationary paradigm has seen its predictions largely unchallenged. A recent proposal, called the ekpyrotic scenario, was argued to be a viable competitor as it was claimed that the spectrum of primordial perturbations it produces is scale invariant. By investigating closely this scenario, we show that the corresponding spectrum depends explicitly on an arbitrary function of wavenumber and is therefore itself arbitrary. It can at will be set scale invariant. We conclude that the scenario is not predictive at this stage.Comment: 4 pages, no figure, uses moriond.sty, to appear in the proceeding of the Moriond cosmology meeting held at Les Arcs, France (March 16-23, 2002

Comments on the Quantum Potential Approach to a Class of Quantum Cosmological Models

In this comment we bring attention to the fact that when we apply the ontological interpretation of quantum mechanics, we must be sure to use it in the coordinate representation. This is particularly important when canonical tranformations that mix momenta and coordinates are present. This implies that some of the results obtained by A. B\l aut and J. Kowalski-Glikman are incorrect.Comment: 7 pages, LaTe

Gaussian superpositions in scalar-tensor quantum cosmological models

A free scalar field minimally coupled to gravity model is quantized and the Wheeler-DeWitt equation in minisuperspace is solved analytically, exhibiting positive and negative frequency modes. The analysis is performed for positive, negative and zero values of the curvature of the spatial section. Gaussian superpositions of the modes are constructed, and the quantum bohmian trajectories are determined in the framework of the Bohm-de Broglie interpretation of quantum cosmology. Oscillating universes appear in all cases, but with a characteristic scale of the order of the Planck scale. Bouncing regular solutions emerge for the flat curvature case. They contract classically from infinity until a minimum size, where quantum effects become important acting as repulsive forces avoiding the singularity and creating an inflationary phase, expanding afterwards to an infinite size, approaching the classical expansion as long as the scale factor increases. These are non-singular solutions which are viable models to describe the early Universe.Comment: 14 pages, LaTeX, 3 Postscript figures, uses graficx.st