Spectra of primordial fluctuations in two-perfect-fluid regular bounces

We introduce analytic solutions for a class of two components bouncing models, where the bounce is triggered by a negative energy density perfect fluid. The equation of state of the two components are constant in time, but otherwise unrelated. By numerically integrating regular equations for scalar cosmological perturbations, we find that the (would be) growing mode of the Newtonian potential before the bounce never matches with the the growing mode in the expanding stage. For the particular case of a negative energy density component with a stiff equation of state we give a detailed analytic study, which is in complete agreement with the numerical results. We also perform analytic and numerical calculations for long wavelength tensor perturbations, obtaining that, in most cases of interest, the tensor spectral index is independent of the negative energy fluid and given by the spectral index of the growing mode in the contracting stage. We compare our results with previous investigations in the literature.Comment: 11 pages, 5 figure

Covariant Bardeen Perturbation Formalism

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem. Using our mixed and pure tensors approach, we were able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hyper-surface dependence inherent to the covariant approach. Finally, through the use of this map, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables $\Phi$, $\Psi$ and $\Xi$, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hyper-surface invariant variables at any order.Comment: 15 pages, no figures, revtex4-1, accepted for publication in PRD, typos fixed, improved discussion about higher order gauge and foliation invarianc

Graceful exit from inflation using quantum cosmology

A massless scalar field without self interaction and string coupled to gravity is quantized in the framework of quantum cosmology using the Bohm-de Broglie interpretation. Gaussian superpositions of the quantum solutions of the corresponding Wheeler-DeWitt equation in minisuperspace are constructed. The bohmian trajectories obtained exhibit a graceful exit from the inflationary Pre-Big Bang epoch to the decelerated expansion phase.Comment: 8 pages, RevTeX, 4 Postscript figures, uses graficx.sty. Added more text and reference

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

Large classical universes emerging from quantum cosmology

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.Comment: 8 pages, 1 figur