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The Hubble constant inferred from the 6-parameter fit to the CMB power spectrum conflicts with the value obtained from direct measurements via type Ia supernova and Cepheids observations. We write down effective operators involving spin-0, spin-1/2, and spin-1 dark matter that lead to the relativistic production of dark matter particles at early times, and consequently lead to an increase in the number of relativistic degrees of freedom. This mechanism which is amenable to CMB, BBN, and structure formation observables can sufficiently raise the value of the Hubble constant derived from CMB and reconcile local and CMB probes of the Hubble constant. This mechanism alone increases $H_0$ up to $70\, {\rm km s^{-1} Mpc^{-1}}$, and with the help of a Phantom-like cosmology, reach $H_0 \simeq 71-73\, {\rm km s^{-1} Mpc^{-1}}$. Lastly, we outline the region of parameter space which reproduces $H_0 \simeq 71-73\, {\rm km s^{-1} Mpc^{-1}}$ while obeying all relevant constraints., 10 pages and 14 figures

In the context of de Broglie-Bohm pilot-wave theory, violations of the Born rule are allowed and can be considered as describing nonequilibrium distributions. We study the effects of interactions on quantum relaxation towards equilibrium for a system of one-dimensional coupled harmonic oscillators. We show by numerical simulations that interactions can delay or even prevent complete relaxation for some initial states. We also discuss how this effect might be relevant for cosmological scenarios and how nonequilibrium could be detected in some models., 15 pages, 7 figures

The problem of finding a vacuum definition for a single quantum field in curved space-times is discussed under a new geometrical perspective. The phase space dynamics of the quantum field modes are mapped to curves in a 2-dimensional hyperbolic metric space, in which distances between neighbor points are shown to be proportional to the Bogoliubov coefficients associated with their corresponding mode solutions in phase space. The vacuum state for each mode is then defined as the unique trajectory from which all mapped phase space solutions move within thin annular regions around it. This property implies the stability of the vacuum state: solutions evolved from a point in this trajectory stay close to it as both evolve, and the particle creation is therefore minimized. The new approach is applied to the well-known cases of the time-independent dynamics, where the solutions draw circles around this curve, and when the adiabatic approximation is valid. The analysis is then extended to time-dependent cases in which the adiabatic approximation is not applicable, in the super-Hubble or low-frequency regimes. It is shown that stability trajectories can also be found in these situations, and stable quantum vacua can be obtained. This new formalism is applied to two situations: de Sitter space, where the Bunch-Davies vacuum is obtained in a completely different manner through an analysis in the super-Hubble regime, and in the context of cosmological bouncing models, in which the contracting phase is dominated by a cosmological constant in the asymptotic past. A new vacuum state for cosmological perturbations is proposed in this situation., Comment: 31 pages, 6 figures

In general, to avoid a singularity in cosmological models involves the introduction of exotic kind of matter fields, for example, a scalar field with negative energy density. In order to have a bouncing solution in classical General Relativity, violation of the energy conditions is required. In this work, we discuss a case of the bouncing solution in the Brans-Dicke theory with radiative fluid that obeys the energy conditions, and with no ghosts., 5 pages, 2 figures, accepted for publication in JETP Letters

In this paper we compute the CMB bispectrum for bouncing models motivated by Loop Quantum Cosmology. Despite the fact that the primordial bispectrum of these models is decaying exponentially above a large pivot scale, we find that the cumulative signal-to-noise ratio of the bispectrum induced in the CMB from scales $\ell < 30$ is larger than $10$ in all cases of interest and therefore can, in principle, be detected in the Planck data., 15 pages, 8 figures. This is the Accepted Manuscript version of an article accepted for publication in Journal of Cosmology and Astroparticle Physics. Neither SISSA Medialab Srl nor IOP Publishing Ltd is responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at the DOI link below

We review the de Broglie-Bohm quantum theory. It is an alternative description of quantum phenomena in accordance with all the quantum experiments already performed. Essentially, it is a dynamical theory about objectively real trajectories in the configuration space of the physical system under investigation. Hence, it is not necessarily probabilistic, and it dispenses with the collapse postulate, making it suitable to be applied to cosmology. The emerging cosmological models are usually free of singularities, with a bounce connecting a contracting era with an expanding phase, which we are now observing. A theory of cosmological perturbations can also be constructed under this framework, which can be successfully confronted with current observations, and can complement inflation or even be an alternative to it., Comment: 34 pages, 9 figures

Classical mechanics for individual physical systems and quantum mechanics of non-relativistic particles are shown to be exceptional cases of a generalized dynamics described in terms of maps between two manifolds, the source being configuration space. The target space is argued to be 2-dimensional and flat, and their orthogonal directions are physically interpreted. All terms in the map equation have a geometrical meaning in the target space, and the pull-back of its rotational Killing one-form allows the construction of a velocity field in configuration space. Identification of this velocity field with tangent vectors in the source space leads to the dynamical law of motion. For a specific choice of an arbitrary scalar function present in the map equation, and using Cartesian coordinates in the target space, the map equation becomes linear and can be reduced to the Schr\"odinger equation. We link the bi-dimensionality of the target space with the essential non-locality of quantum mechanics. Many extensions of the framework here presented are immediate, with deep consequences yet to be explored., Comment: The version accepted in PRD

We show how to systematically apply the Faddeev-Jackiw symplectic method to General Relativity (GR) and to GR extensions. This provides a new coherent frame for Hamiltonian analyses of gravitational theories. The emphasis is on the classical dynamics, uncovering the constraints, the gauge transformations and the number of degrees of freedom; but the method results are also relevant for canonical quantization approaches. We illustrate the method with three applications: GR and to two Brans-Dicke cases (the standard case $\omega \not= - 3/2$ and the case with one less degree of freedom, $\omega = - 3/2$). We clarify subtleties of the symplectic approach and comment on previous symplectic-based Hamiltonian analyses of extended theories of gravity, pointing out that the present approach is systematic, complete and robust., Comment: 31 pages. v2: added comments. Version to appear in Phys.Rev.D

Analyzing quantum cosmological scenarios containing one scalar field with exponential potential, we have obtained a universe model which realizes a classical dust contraction from very large scales, the initial repeller of the model, and moves to a stiff matter contraction near the singularity, which is avoided due to a quantum bounce. The universe is then launched in a stiff matter expanding phase, which then moves to a dark energy era, finally returning to the dust expanding phase, the final attractor of the model. Hence one has obtained a nonsingular cosmological model where a single scalar field can describe both the matter contracting phase of a bouncing model, necessary to give an almost scale invariant spectrum of scalar cosmological perturbations, and a transient expanding dark energy phase. As the universe is necessarily dust dominated in the far past, usual adiabatic vacuum initial conditions can be easily imposed in this era, avoiding the usual issues appearing when dark energy is considered in bouncing models., 15 pages, 17 figures. Title changed, introduction, conclusion and bibliography expanded to answer the questions of a referee. To be published in Physical Review D

We investigate cosmological scenarios containing one canonical scalar field with an exponential potential in the context of bouncing models, where the bounce happens due to quantum cosmological effects. The only possible bouncing solutions in this scenario (discarding an infinitely fine tuned exception) must have one and only one dark energy phase, either occurring in the contracting era or in the expanding era. Hence,these bounce solutions are necessarily asymmetric. We calculate the spectral indexes and amplitudes of scalar and tensor perturbations numerically, considering the whole history of the model, including the bounce phase itself, without making any approximation or using any matching condition on the perturbations. As the background model is necessarily dust dominated in the far past, the usual adiabatic vacuum initial conditions can be easily imposed in this era. Hence, this is a cosmological model where the presence of dark energy behavior in the Universe does not turn problematic the usual vacuum initial conditions prescription for cosmological perturbation in bouncing models. Scalar and tensor perturbations end up being almost scale invariant, as expected. The background parameters can be adjusted, without fine tunings, to yield the observed amplitude for scalar perturbations, and also for the ratio between tensor and scalar amplitudes, $r = T/S \lesssim 0.1$. The amplification of scalar perturbations over tensor perturbations takes place only around the bounce, due to quantum effects, and it would not occur if General Relativity has remained valid throughout this phase. Hence, this is a bouncing model where a single field induces not only an expanding background dark energy phase, but also produces all observed features of cosmological perturbations of quantum mechanical origin at linear order., Comment: 23 pages, 15 figures

Bouncing models have been proposed by many authors as a completion, or even as an alternative to inflation for the description of the very early and dense Universe. However, most bouncing models contain a contracting phase from a very large and rarefied state, where dark energy might have had an important role as it has today in accelerating our large Universe. In that case, its presence can modify the initial conditions and evolution of cosmological perturbations, changing the known results already obtained in the literature concerning their amplitude and spectrum. In this paper, we assume the simplest and most appealing candidate for dark energy, the cosmological constant, and evaluate its influence on the evolution of cosmological perturbations during the contracting phase of a bouncing model, which also contains a scalar field with a potential allowing background solutions with pressure and energy density satisfying p = w*rho, w being a constant. An initial adiabatic vacuum state can be set at the end of domination by the cosmological constant, and an almost scale invariant spectrum of perturbations is obtained for w~0, which is the usual result for bouncing models. However, the presence of the cosmological constant induces oscillations and a running towards a tiny red-tilted spectrum for long wavelength perturbations., Comment: 11 pages, 11 figures

We investigate scalar particle creation in a set of bouncing models where the bounce occurs due to quantum cosmological effects described by the Wheeler-DeWitt equation. The scalar field can be either conformally or minimally coupled to gravity, and it can be massive or massless, without self interaction. The analysis is made for models containing a single radiation fluid, and for the more realistic case of models containing the usual observed radiation and dust fluids, which can fit most of the observed features of our Universe, including an almost scale invariant power spectrum of scalar cosmological perturbations. In the conformal coupling case, the particle production is negligible. In the minimal coupling case, for massive particles, the results point to the same physical conclusion within observational constraints: particle production is most important at the bounce energy scale, and it is not sensitive neither to its mass nor whether there is dust in the background model. The only caveat is the case where the particle mass is larger than the bounce energy scale. On the other hand, the energy density of produced massive particles depend on their masses and the energy scale of the bounce. For very large masses and deep bounces, this energy density may overcome that of the background. In the case of massless particles, the energy density of produced particles can become comparable to the background energy density only for bounces occurring at energy scales comparable to the Planck scale or above, which lies beyond the scope of this paper: we expect that the simple Wheeler-DeWitt approach we are using should be valid only at scales some few orders of magnitude below the Planck energy. Nevertheless, in the case in which dust is present, there is an infrared divergence, which becomes important only for scales much larger than today's Hubble radius., Comment: 18 pages, 8 figures

In this paper we study in details a system of two weakly coupled harmonic oscillators. This system may be viewed as a simple model for the interaction between a photon and a photodetector. We obtain exact solutions for the general case. We then compute approximate solutions for the case of a single photon (where one oscillator is initially in its first excited state) reaching a photodetector in its ground state (the other oscillator). The approximate solutions represent the state of both the photon and the photodetector after the interaction, which is not an eigenstate of the individual hamiltonians for each particle, and therefore the energies for each particle do not exist in the Copenhagen interpretation of Quantum Mechanics. We use the approximate solutions that we obtained to compute bohmian trajectories and to study the energy transfer between the two particles. We conclude that even using the bohmian view the energy of each individual particle is not well defined, as the nonlocal quantum potential is not negligible even after the coupling is turned off., Comment: 18 pages, 5 figures

The causal interpretation of quantum mechanics is applied to a homogeneous and isotropic quantum universe, whose matter content is composed by non interacting dust and radiation. For wave functions which are eigenstates of the total dust mass operator, we find some bouncing quantum universes which reachs the classical limit for scale factors much larger than its minimum size. However these wave functions do not have unitary evolution. For wave functions which are not eigenstates of the dust total mass operator but do have unitary evolution, we show that, for flat spatial sections, matter can be created as a quantum effect in such a way that the universe can undergo a transition from an exotic matter dominated era to a matter dominated one., Comment: 27 pages, 6 figures

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., Comment: 28 pages, 1 figure, contribution to the James Cushing festschrift to appear in Foundations of Physics

I describe the features and general properties of bouncing models and the evolution of cosmological perturbations on such backgrounds. I will outline possible observational consequences of the existence of a bounce in the primordial Universe and I will make a comparison of these models with standard long inflationary scenarios., 9 pages, no figures

We study the quantized Friedmann-Lema\^��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

We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaitre-Robertson-Walker model and investigate the question whether or not there are singularities, in the sense that the universe reaches zero volume. We find that for generic wave functions (i.e., non-classical wave functions), there is a non-zero probability for a trajectory to be non-singular. This should be contrasted to the consistent histories approach for which it was recently shown by Craig and Singh that there is always a singularity. This result illustrates that the question of singularities depends much on which version of quantum theory one adopts. This was already pointed out by Pinto-Neto et al., albeit with a different Bohmian approach. Our current Bohmian approach agrees with the consistent histories approach by Craig and Singh for single-time histories, unlike the one studied earlier by Pinto-Neto et al. Although the trajectories are usually different in the two Bohmian approach, their qualitative behavior is the same for generic wave functions., Comment: 10 pages, 3 figures, PDFLaTeX, revtex4

The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid)., Comment: 20 pages, matches PRD published version

We apply the causal interpretation of quantum mechanics to homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces have positive curvature. In order to simplify the system of coupled equations studied and study the quantum behavior near the singularity, we restricted ourselves to the cases where the scale factor is small. In this case, the general solution of the Wheeler–DeWitt equation is a discrete superposition of Hermitian polynomials multiplied by complex exponentials. Superpositions with up to two parcels are studied, and the phase diagrams of their corresponding Bohmian trajectories are analyzed in detail. Nonsingular periodic quantum solutions are found. We also find that singular quantum solutions present an inflationary era in the begining of the Universe. Numerical calculations indicates that these results remain valid for general superpositions.

We apply the causal interpretation of quantum mechanics to homogeneous and isotropic quantum cosmology where the sources of the gravitational field are either dust or radiation perfect fluids. We find non-singular quantum trajectories which tends to the classical one when the scale factor becomes much larger then the Planck length. In this situation, the quantum potential becomes negligible. There are no horizons. As radiation is a good approximation for the matter content of the early universe, this result suggests that the universe can be eternal due to quantum effects., 10 pages, LaTeX, 5 figures in postscript, requires epsf

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

Recently it has been claimed that the Wheeler-DeWitt quantization of gravity is unable to avoid cosmological singularities. However, in order to make this assertion, one must specify the underlying interpretation of quantum mechanics which has been adopted. For instance, several nonsingular models were obtained in Wheeler-DeWitt quantum cosmology in the framework of the de Broglie-Bohm quantum theory. Conversely, there are specific situations where the singularity cannot be avoided in the framework of the Consistent Histories approach to quantum mechanics. In these specific situations, the matter content is described by a scalar field, and the Wheeler-DeWitt equation looks-like a Klein-Gordon equation. The aim of this work is to study the Wheeler-DeWitt quantization of cosmological models where the matter content is described by an hydrodynamical perfect fluid, where the Wheeler-DeWitt equation reduces to a genuine Schr\"odinger equation. In this case, it is shown that the conclusions of the Consistent Histories and the de Broglie-Bohm approaches coincide in the quantum cosmological models where the curvature of the spatial sections is not positive definite, namely, that the cosmological singularities are eliminated. In the case of positive spatial curvature, the family of histories is no longer consistent, and no conclusion can be given in this framework., Comment: 11 pages, 4 figures

In a previous work we have exhibited a clear description of the quantum-to-classical transition of cosmological quantum fluctuations in the inflationary scenario using the de Broglie-Bohm quantum theory. These fluctuations are believed to seed the small inhomogeneities, which are then responsible for the formation of large scale structures. In this work we show that using the de Broglie-Bohm theory it is also possible to describe the quantum-to-classical transition of primordial perturbations which takes place around a bouncing phase, even if the latter is caused by quantum effects due to the quantization of the background geometry., Comment: 5 pages, no figures, revtex4

We examine the nonlinear dynamics of a closed Friedmann-Robertson-Walker universe in the framework of Brane World formalism with a timelike extra dimension. In this scenario, the Friedmann equations contain additional terms arising from the bulk-brane interaction which provide a concrete model for nonsingular bounces in the early phase of the Universe. We construct a nonsingular cosmological scenario sourced with dust, radiation and a cosmological constant. The structure of the phase space shows a nonsingular orbit with two accelerated phases, separated by a smooth transition corresponding to a decelerated expansion. Given observational parameters we connect such phases to a primordial accelerated phase, a soft transition to Friedmann (where the classical regime is valid), and a graceful exit to a de Sitter accelerated phase.

A quantum cosmological model with radiation and a dilaton scalar field is analysed. The Wheeler-deWitt equation in the mini-superspace induces a Schr\"odinger equation, which can be solved. An explicit wavepacket is constructed for a particular choice of the ordering factor. A consistent solution is possible only when the scalar field is a phantom field. Moreover, although the wavepacket is time dependent, a Bohmian analysis allows to extract a bouncing behaviour for the scale factor., Comment: 14 pages, 3 figures in eps format. Minors corrections, new figures

We study the Wheeler-DeWitt quantum cosmology of a spatially flat Friedmann cosmological model with a massless free scalar field. We compare the consistent histories approach with the de Broglie-Bohm theory when applied to this simple model under two different quantization schemes: the Schr\"odinger-like quantization, which essentially takes the square-root of the resulting Klein-Gordon equation through the restriction to positive frequencies and their associated Newton-Wigner states, or the induced Klein-Gordon quantization, that allows both positive and negative frequencies together. We show that the consistent histories approach can give a precise answer to the question concerning the existence of a quantum bounce if and only if one takes the single frequency approach and within a single family of histories, namely, a family containing histories concerning properties of the quantum system at only two specific moments of time: the infinity past and the infinity future. In that case, as shown by Craig and Singh \cite{CS}, there is no quantum bounce. In any other situation, the question concerning the existence of a quantum bounce has no meaning in the consistent histories approach. On the contrary, we show that if one considers the de Broglie-Bohm theory, there are always states where quantum bounces occur in both quantization schemes. Hence the assertion that the Wheeler-DeWitt quantization does not solve the singularity problem in cosmology is not precise. To address this question, one must specify not only the quantum interpretation adopted but also the quantization scheme chosen., Comment: 13 pages, 1 figure

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., 10 pages, 2 figures, accepted version to Physical Review D 79

In previous works, it was shown that the Lagrangians and Hamiltonians of cosmological linear scalar, vector and tensor perturbations of homogeneous and isotropic space-times with flat spatial sections containing a perfect fluid can be put in a simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. In this paper, we generalize this result to general fluids, which includes entropy perturbations, and to arbitrary spacelike hyper-surfaces through a new method together with the Faddeev-Jackiw procedure for the constraint reduction. A simple second order Hamiltonian involving the Mukhanov-Sasaki variable is obtained, again without ever using the background equations of motion., Comment: 19 pages, revtex4-1, submitted to PRD, expanded discussion about our method, fixed typos

There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this paper, we show how these issues can easily be overcome in the framework of the de Broglie-Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit., 5 pages, no figures, REVTeX

It has been shown that a contracting universe with a dust-like ($w \approx 0$) fluid may provide an almost scale invariant spectrum for the gravitational scalar perturbations. As the universe contracts, the amplitude of such perturbations are amplified. The gauge invariant variable $\Phi$ develops a growing mode which becomes much larger than the constant one around the bounce phase. The constant mode has its amplitude fixed by Cosmic Background Explorer (COBE) normalization, thus the amplitude of the growing mode can become much larger than 1. In this paper, we first show that this is a general feature of bouncing models, since we expect that general relativity should be valid in all scales away from the bounce. However, in the Newtonian gauge, the variable $\Phi$ gives the value of the metric perturbation $\phi$, raising doubts on the validity of the linear perturbative regime at the bounce. In order to address this issue, we obtain a set of necessary conditions for the perturbative series to be valid along the whole history of the model, and we show that there is a gauge in which all these conditions are satisfied, for a set of models, if the constant mode is fixed by COBE normalization. As a by-product of this analysis, we point out that there are sets of solutions for the perturbation variables where some gauge-fixing conditions are not well defined, turning these gauges prohibited for those solutions., Comment: 10 pages, revtex4, minor revision, version to appear in PRD

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

Recent investigations seem to favor a cosmological dynamics according to which the accelerated expansion of the Universe may have already peaked and is now slowing down again \cite{sastaro}. As a consequence, the cosmic acceleration may be a transient phenomenon. We investigate a toy model that reproduces such a background behavior as the result of a time-dependent coupling in the dark sector which implies a cancelation of the "bare" cosmological constant. With the help of a statistical analysis of Supernova Type Ia (SNIa) data we demonstrate that for a certain parameter combination a transient accelerating phase emerges as a pure interaction effect., Comment: Latex file, 23 pages, 21 figures in eps format. Discussion enlarged, new subsection on scalar field dynamics included, accepted for publication in JCAP.

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., 8 pages, no figure

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., 11 pages, 5 figures

Cosmological models with two interacting fluids, each satisfying the strong energy condition, are studied in the framework of classical General Relativity. If the interactions are phenomenologically described by a power law in the scale factor, the two initial interacting fluids can be equivalently substituted by two non interacting effective fluids, where one of them may violate the strong energy condition and/or have negative energy density. Analytical solutions of the Friedmann equations of this general setting are obtained and studied. One may have, depending on the scale where the interaction becomes important, non singular universes with early accelerated phase, or singular models with transition from decelerated to accelerated expansion at large scales. Among the first, there are bouncing models where contraction is stopped by the interaction. In the second case, one obtains dark energy expansion rates without dark energy, like $\Lambda$CDM or phantomic accelerated expansions without cosmological constant or phantoms, respectively., Comment: 10 pages, no figures, accepted for publication in General Relativity and Gravitation

We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-de Witt equation, thus treating both the background and the perturbations in a fully quantum manner. We find a very slightly blue spectrum ($n_{_\mathrm{S}}-1>0$). Taking into account the spectral index constraint as well as the CMB normalization measure yields an equation of state that should be less than $\omega\lesssim 8\times 10^{-4}$, implying $n_{_\mathrm{S}}-1 \sim \mathcal{O}(10^{-4})$, and that the characteristic size of the Universe at the bounce is $L_0 \sim 10^3 \ell_\mathrm{Planck}$, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects., Comment: 9 pages, 4 figures

Generalizing a previous work concerning cosmological linear tensor perturbations, we show that the lagrangians and hamiltonians of cosmological linear scalar and vector perturbations can be put in simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. In particular, if the matter content of the Universe is a perfect fluid, the hamiltonian of scalar perturbations can be reduced, as usual, to a hamiltonian of a scalar field with variable mass depending on background functions, independently of the fact that these functions satisfy the background Einstein's classical equations. These simple lagrangians and hamiltonians can then be used in situations where the background metric is also quantized, hence providing a substantial simplification over the direct approach originally developed by Halliwell and Hawking., 19 pages, no figure

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., 12 pages, 5 figures, to appear in Phys. Rev. D (2006)

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, LaTeX

In the description of the dynamics of tensor perturbations on a homogeneous and isotropic background cosmological model, it is well known that a simple Hamiltonian can be obtained if one assumes that the background metric satisfies Einstein classical field equations. This makes it possible to analyze the quantum evolution of the perturbations since their dynamics depends only on this classical background. In this paper, we show that this simple Hamiltonian can also be obtained from the Einstein-Hilbert lagrangian without making use of any assumption about the dynamics of the background metric. In particular, it can be used in situations where the background metric is also quantized, hence providing a substantial simplification over the direct approach originally developed by Halliwell and Hawking., Comment: 24 pages, JHEP format

We obtain the correct hamiltonian which describes the dynamics of classes of asymptotic open Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetimes, which includes Tolman geometries. We calculate the surface term that has to be added to the usual hamiltonian of General Relativity in order to obtain an improved hamiltonian with well defined functional derivatives. For asymptotic flat FLRW spaces, this surface term is zero, but for asymptotic negative curvature FLRW spaces it is not null in general. In the particular case of the Tolman geometries, they vanish. The surface term evaluated on a particular solution of Einstein's equations may be viewed as the ``energy'' of this solution with respect to the FLRW spacetime they approach asymptotically. Our results are obtained for a matter content described by a dust fluid, but they are valid for any perfect fluid, including the cosmological constant., Comment: 12 pages, no figures

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

The possibility of obtaining singularity free cosmological solutions in four dimensional effective actions motivated by string theory is investigated. In these effective actions, in addition to the Einstein-Hilbert term, the dilatonic and the axionic fields are also considered as well as terms coming from the Ramond-Ramond sector. A radiation fluid is coupled to the field equations, which appears as a consequence of the Maxwellian terms in the Ramond-Ramond sector. Singularity free bouncing solutions in which the dilaton is finite and strictly positive are obtained for models with flat or negative curvature spatial sections when the dilatonic coupling constant is such that $\omega < - 3/2$, which may appear in the so called $F$ theory in 12 dimensions. These bouncing phases are smoothly connected to the radiation dominated expansion phase of the standard cosmological model, and the asymptotic pasts correspond to very large flat spacetimes., Comment: 10 pages, ReVTeX format, 2 figures, to appear in Phys. Rev. D (2003)

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

We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative hamiltonian method, a concrete example where Lorentz invariance of individual events is broken., Final version. See also http://www.cosmologia.cbpf.br

We consider minisuperspace models constituted of Bianchi I geometries with a free massless scalar field. The classical solutions are always singular (with the trivial exception of flat space-time), and always anisotropic once they begin anisotropic. When quantizing the system, we obtain the Wheeler-DeWitt equation as a four-dimensional massless Klein-Gordon equation. We show that there are plenty of quantum states whose corresponding bohmian trajectories may be non-singular and/or presenting large isotropic phases, even if they begin anisotropic, due to quantum gravitational effects. As a specific example, we exhibit field plots of bohmian trajectories for the case of gaussian superpositions of plane wave solutions of the Wheeler-DeWitt equation which have those properties. These conclusions are valid even in the absence of the scalar field., 10 pages, RevTeX, 3 Postscript figures, uses graficx.sty

Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form, which corresponds to the minimal coupling case, whose general solution is known. Performing the inverse conformal transformation in the solution so found, we can construct the corresponding one in the original frame. This procedure can also be employed with the bohmian trajectories. In this way, we can study the classical limit of some solutions of this quantum model. While the classical limit of these solutions occurs for small scale factors in the Einstein's frame, it happens for small values of the scalar field non minimally coupled to gravity in the Jordan's frame, which includes large scale factors., Comment: latex, 18 pages