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It is widely known that bouncing models with a dust hydrodynamical fluid satisfying ${c_s^2=p_d/\rho_d\approx 0}$, where $c_s, p_d, \rho_d$ are the sound velocity, pressure and energy density of the dust fluid, respectively, have almost scale invariant spectrum of scalar perturbations and negligible primordial gravitational waves. We investigate whether adding another fluid with $1/3 < \lambda = p/\rho < 1$, which should dominate near the bounce, can increase the amplitude of gravitational waves in the high frequency regime, turning them detectable in near future observations for such range of frequencies. Indeed, we show that the energy density of primordial gravitational waves is proportional to $k^{2(9\lambda-1)/(1+3\lambda)}$ for wavelengths which become bigger than the Hubble radius when this extra fluid dominates the background. Hence, as $\lambda \to 1$ (an almost stiff matter fluid), the energy density of primordial gravitational waves will increase faster in frequency, turning them potentially detectable at high frequencies. However, there is an extra factor $I_q(\lambda)$ in the amplitude which decreases exponentially with $\lambda$. The net effect of these two contributions turns the energy density of primordial gravitational waves not sufficiently big at high frequencies in order to be detected by present day or near future observations for models which satisfy the nucleosynthesis bounds and is symmetric with respect to the bounce. Hence, symmetric bouncing models where the background is dominated by a dust hydrodynamical fluid with small sound velocity, do not present any significant amount of primordial gravitational waves at any frequency range compatible with observations, even if there are other fields present in the model dominating the bounce phase. Any detection of such waves will then rule out this kind of models.

Minisuperspace models derived from Kaluza-Klein theories and low-energy string theory are studied. They are equivalent to one and two minimally coupled scalar fields. The general classical and quantum solutions are obtained. A Gaussian superposition of WKB solutions is constructed. Contrary to what is usually expected, these states are sharply peaked around the classical trajectories only for small values of the scale factor. This behavior is confirmed in the framework of the causal interpretation: the Bohmian trajectories of many quantum states are classical for small values of the scale factor but present quantum behavior when the scale factor becomes large. A consequence of this fact is that these states present an initial singularity. However, there are some particular superpositions of these wave functions which have Bohmian trajectories without singularities. There are also singular Bohmian trajectories with a short period of inflation which grow forever. We could not find any nonsingular trajectory which grows to the size of our universe.

A recent paper by Kumar (2012) (hereafter K12) claimed that in a contracting model, described by perturbations around a collapsing Friedmann model containing dust or radiation, the perturbations can grow in such a way that the linearity conditions would become invalid. This conclusion is not correct due to the following facts: first, it is claimed that the linearity conditions are not satisfied, but nowhere in K12 the amplitudes of the perturbations were in fact estimated. Therefore, without such estimates, the only possible conclusion from this work is the well-known fact that the perturbations indeed grow during contraction, which, per se, does not imply that the linearity conditions become invalid. Second, some evaluations of the linearity conditions are incorrect because third-order terms, instead of the appropriate second-order ones, are mistakenly compared with first-order terms, yielding artificially fast growing conditions. Finally, it is claimed that the results of K12 are in sharp contrast with the results of the paper by Vitenti and Pinto-Neto (2012) (hereafter VPN12), because the former was obtained in a gauge-invariant way. However, the author of K12 did not realize that the evolution of the perturbations were also calculated in a gauge-invariant way in VPN12, but some of the linearity conditions which are necessary to check cannot be expressed in terms of gauge-invariant quantities. In the present work, the incorrect or incomplete statements of K12 are clarified and completed, and it is shown that all other correct results of K12 were already present in VPN12, whose conclusions remain untouched, namely, that cosmological perturbations of quantum mechanical origin in a bouncing model can remain in the linear regime all along the contracting phase and at the bounce itself for a wide interval of energy scales of the bounce, ranging from the nucleosynthesis energy scale up to a few orders of magnitude below the Planck energy.

We develop the canonical quantization of a midisuperspace model which contains, as a subspace, a minisuperspace constituted of a Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar and dust fields, where the sign of the intrinsic curvature of the spacelike hypersurfaces of homogeneity is not specified, allowing the study of topology change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the midisuperspace model restricted to this minisuperspace subspace in the semi-classical approximation. Adopting the conditional probability interpretation, we find that some of the solutions present change of topology of the homogeneous hypersurfaces. However, this result depends crucially on the interpretation we adopt: using the usual probabilistic interpretation, we find selection rules which forbid some of these topology changes., Comment: 23 pages, LaTex file. We added in the conclusion some comments about path integral formalism and corrected litle misprintings

The prescription proposed by Komar in order to calculate the total gravitational mass acting on a test particle in a given stationary asymptotically flat spacetime is generalized to stationary asymptotically anti\char21{}de Sitter spacetimes. It is shown that this generalized Komar mass is different from the total gravitational energy calculated by Henneaux and Teitelboim for the Kerr\char21{}anti-de Sitter spacetime. This last total energy agrees, however, with the total charge-energy calculated using the Brown-York action formalism.

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., Comment: 11 pages, 6 figures, published in Phys. Rev. D

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 figure

We show that phantom dark energy, if it is described by a k-essence theory, has three fundamental problems: first, its Hamiltonian is unbounded from below. Second, classical stability precludes the equation of state from crossing the 'Lambda-barrier', w{sub {lambda}}=-1. Finally, both the equation of state and the sound speed are unbounded - the first, from below, the second, from above - if the kinetic term is not bounded by dynamics.

In the paper ``Density perturbations in the ekpyrotic scenario'', it is argued that the expected spectrum of primordial perturbations should be scale invariant in this scenario. Here we show that, contrary to what is claimed in that paper, the expected spectrum depends on an arbitrary choice of matching variable. As no underlying (microphysical) principle exists at the present time that could lift the arbitrariness, we conclude that the ekpyrotic scenario is not yet a predictive model., Comment: 4 pages, no figure, RevTeX, commenting on hep-th/0109050

We construct a simple non singular cosmological model in which the currently observed expansion phase was preceded by a contraction. This is achieved, in the framework of pure general relativity, by means of a radiation fluid and a free scalar field having negative energy. We calculate the power spectrum of the scalar perturbations that are produced in such a bouncing model and find that, under the assumption of initial vacuum state for the quantum field associated with the hydrodynamical perturbation, this leads to a spectral index n=-1. The matching conditions applying to this bouncing model are derived and shown to be different from those in the case of a sharp transition. We find that if our bounce transition can be smoothly connected to a slowly contracting phase, then the resulting power spectrum will be scale invariant., Comment: 11 pages, RevTeX 4, 8 figures, submitted to Phys. Rev. D

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.sty