arXiv subjects

A. B. Batista

Publications and source records attributed to A. B. Batista.

17 recordsLinked to original sources

arXiv2016

Quantum cosmology of scalar-tensor theories and self-adjointness

In this paper, the problem of the self-adjointness for the case of a quantum minisuperspace Hamiltonian retrieved from a Brans-Dicke (BD) action is investigated. Our matter content is presented in terms of a perfect fluid, onto which the Schutz's formalism will be applied. We use the von Neumann theorem and the similarity with the Laplacian operator in one of the variables to determine the cases where the Hamiltonian is self-adjoint and if it admits self-adjoint extensions. For the latter, we study which extension is physically more suitable.

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arXiv2015

Quantum cosmology with scalar fields: self-adjointness and cosmological scenarios

We discuss the issue of unitarity in particular quantum cosmological models with scalar field. The time variable is recovered, in this context, by using the Schutz's formalism for a radiative fluid. Two cases are considered: a phantom scalar field and an ordinary scalar field. For the first case, it is shown that the evolution is unitary provided a convenient factor ordering and inner product measure are chosen; the same happens for the ordinary scalar field, except for some special cases for which the Hamiltonian is not self-adjoint but admits a self-adjoint extension. In all cases, even for those cases not exhibiting unitary evolution, the formal computation of the expectation value of the scale factor indicates a non-singular bounce. The importance of the unitary evolution in quantum cosmology is briefly discussed.

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arXiv2012

Sudden singularities survive massive quantum particle production

We solve the Klein-Gordon equation for a massive, non-minimally coupled scalar field, with a conformal coupling, undergoing cosmological evolution from a radiation-dominated phase to a future sudden singularity. We show that, after regularisation, the energy of the created particles is zero and the back-reaction from quantum effects does not change the evolution of the universe near the future singularity and cannot prevent the finite-time sudden singularity.

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arXiv2009

Quantum particle production near the big rip revisited

The effect of quantum particle production near the big rip singularity has been investigated previously, with the conclusion that the energy of the produced particle decreases as the future singularity is approached. Hence, the effect of particle production would not be effective to avoid the big rip singularity. That calculation was performed by introducing an ultra-violet cut-off. In the present work we consider a renormalization of the energy-momentum tensor, obtainning a different expression for the particle production. The new expression seems to indicate that the effect of particle production may be dominant as the singularity is approached.

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arXiv2007

Particle Production in an expanding universe dominated by dark energy fluid

We investigate the fate of particle production in an expanding universe dominated by a perfect fluid with equation of state $p = αρ$. The rate of particle production, using the Bogolioubov coefficients, are determined exactly for any value of $α$ in the case of a flat universe. When the strong energy condition is satisfied, the rate of particle production decreases as time goes on, in agreement to the fact that the four-dimensional curvature decreases with the expansion; the opposite occurs when the strong energy condition is violated. In the phantomic case, the rate of particle production diverges in a finite time. This may lead to a backreaction effect, leading to the avoidance of the big rip singularity, specially if $- 1 > α> - {5/3}$.

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arXiv2004

Quantum modes around a scalar-tensor black hole: breakdown of the normalization conditions

Black holes arising in the context of scalar-tensor gravity theories, where the scalar field is non-minimally coupled to the curvature term, have zero surface gravity. Hence, it is generally stated that their Hawking temperature is zero, irrespectivelly of their gravitational and scalar charges. The proper analysis of the Hawking temperature requires to study the propagation of quantum fields in the space-time determined by these objects. We study scalar fields in the vicinity of the horizon of these black holes. It is shown that the scalar modes do not form an orthonormal set. Hence, the Hilbert space is ill-definite in this case, and no notion of temperature can be extracted for such objects.

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arXiv2004

Does Quantum Cosmology Predict a Constant Dilatonic Field?

Quantum cosmology may permit to determine the initial conditions of the Universe. In particular, it may select a specific model between many possible classical models. In this work, we study a quantum cosmological model based on the string effective action coupled to matter. The Schutz's formalism is employed in the description of the fluid. A radiation fluid is considered. In this way, a time coordinate may be identified and the Wheeler-DeWitt equation reduces in the minisuperspace to a Schrödinger-like equation. It is shown that, under some quite natural assumptions, the expectation values indicate a null axionic field and a constant dilatonic field. At the same time the scale factor exhibits a bounce revealing a singularity-free cosmological model. In some cases, the mininum value of the scale factor can be related to the value of gravitational coupling.

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arXiv2004

Troubles with quantum anisotropic cosmological models: loss of unitarity

The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. It is shown that the resulting model is non-unitary. This breaks the equivalence between the many-worlds and dBB interpretations of quantum mechanics.

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arXiv2003

Is the semi-classical analysis valid for extreme black holes?

The surface gravity for the extreme Reissner-Nordström black hole is zero suggesting that it has a zero temperature. However, the direct evaluation of the Bogolubov's coefficients, using the standard semi-classical analysis, indicates that the temperature of the extreme black hole is ill definite: the Bogolubov's coefficients obtained by performing the usual analysis of a collapsing model of a thin shell, and employing the geometrical optical approximation, do not obey the normalization conditions. We argue that the failure of the employement of semi-classical analysis for the extreme black hole is due to the absence of orthonormal quantum modes in the vicinity of the event horizon in this particular case.

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arXiv2003

Zero temperature black holes and the failure of semi-classical analysis

The extreme Reissner-Nordström black holes have zero surface gravity. However, a semi-classical analysis seems to be ill-definite for these objects and apparently no notion of temperature exists for them. It is argued here that these properties are shared for all kind of black holes whose surface gravity is zero. Two examples are worked out explicitely: the scalar-tensor cold black holes and extreme black holes resulting from a gravity system coupled to a generalized Maxwell field in higher dimensions. The reasons for this anomolous behaviour are discussed as well as its thermodynamics implications.

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arXiv2003

Troubles with quantum anistropic cosmological models: Loss of unitarity

The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. A Schrödinger-type equation is obtained where the matter variables play the role of time. However, the signature of the kinetic term is hyperbolic. This Schrödinger-like equation is solved and a wave packet is constructed. The norm of the resulting wave function comes out to be time dependent, indicating the loss of unitarity in this model. The loss of unitarity is due to the fact that the effective Hamiltonian is hermitian but not self-adjoint. The expectation value and the bohmian trajectories are evaluated leading to different cosmological scenarios, what is a consequence of the absence of a unitary quantum structure. The consistency of this quantum model is discussed as well as the generality of the absence of unitarity in anisotropic quantum models.

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arXiv2002

Anisotropic quantum cosmological models: a discrepancy between many-worlds and dBB interpretations

In the isotropic quantum cosmological perfect fluid model, the initial singularity can be avoided, while the classical behaviour is recovered asymptotically. We verify if initial anisotropies can also be suppressed in a quantum version of a classical anisotropic model where gravity is coupled to a perfect fluid. Employing a Bianchi I cosmological model, we obtain a "Schrödinger-like" equation where the matter variables play de role of time. This equation has a hyperbolic signature. It can be explicitly solved and a wave packet is constructed. The expectation value of the scale factor, evaluated in the spirit of the many-worlds interpretation, reveals an isotropic Universe. On the other hand, the bohmian trajectories indicate the existence of anisotropies. This is an example where the Bohm-de Broglie and the many-worlds interpretations are not equivalent. It is argued that this inequivalence is due to the hyperbolic structure of the "Schrödinger-like" equation.

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arXiv2001

Quantum cosmological perfect fluid model and its classical analogue

The quantization of gravity coupled to a perfect fluid model leads to a Schrödinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state $p = αρ$; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of $α$, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.

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arXiv2001

On the consistency of a repulsive gravity phase in the early Universe

We exploit the possibility of existence of a repulsive gravity phase in the evolution of the Universe. A toy model with a free scalar field minimally coupled to gravity, but with the "wrong sign" for the energy and negative curvature for the spatial section, is studied in detail. The background solutions display a bouncing, non-singular Universe. The model is well-behaved with respect to tensor perturbations. But, it exhibits growing models with respect to scalar perturbations whose maximum occurs in the bouncing. Hence, large inhomogeneties are produced. At least for this case, a repulsive phase may destroy homogeneity, and in this sense it may be unstable. A newtonian analogous model is worked out; it displays qualitatively the same behaviour. The generality of this result is discussed. In particular, it is shown that the addition of an attractive radiative fluid does not change essentially the results. We discuss also a quantum version of the classical repulsive phase, through the Wheeler-de Witt equation in mini-superspace, and we show that it displays essentially the same scenario as the corresponding attractive phase.

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arXiv2000

Qualitative analysis of a scalar-tensor theory with exponential potential

A qualitative analysis of a scalar-tensor cosmological model, with an exponential potential for the scalar field, is performed. The phase diagram for the flat case is constructed. It is shown that solutions with an initial and final inflationary behaviour appear. The conditions for which the scenario favored by supernova type Ia observations becomes an attractor in the space of the solutions are established.

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arXiv2000

Classical analogous of quantum cosmological perfect fluid models

Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state $p_Q = ρ_Q$ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.

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arXiv2000

A remark on Brans-Dicke dust cosmological solutions with negative $ω$

Analysing the Brans-Dicke solutions for the dust phase, we show that, for negative values of $ω$, they contain scenarios that display an initial subluminal expansion followed by an inflationary phase. We discuss these solutions with respect to the results of the observation of high redshif supernova as well as the age problem and structure formation. We stablish possible connections of these solutions with those emerging from string effective models.

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