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

The Bohm Interpretation of Quantum Cosmology

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 Physic

The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

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.Comment: Final version. See also http://www.cosmologia.cbpf.b

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 Schr\"odinger-type equation is obtained where the matter variables play the role of time. However, the signature of the kinetic term is hyperbolic. This Schr\"odinger-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.Comment: Latex file, 18 pages. To appear in General Relativity and Gravitatio

Potencial pedoclimático do Estado de Alagoas para a cultura do milho (Zea mays L.).

O potencial pedoclimático de ambientes para culturas agrícolas depende, além das condições de solo e clima, da geologia, do relevo (topografia) e de fatores biológicos, associados às exigências das culturas. Este trabalho foi realizado em parceria entre a Embrapa Solos UEP-Recife e a Secretaria de Agricultura e Desenvolvimento Agrário do Estado de Alagoas - SEAGRI-AL. O objetivo deste estudo foi avaliar o potencial pedoclimático do Estado de Alagoas para a cultura do milho (Zea Mays L.). Os resultados deste trabalho são apresentados considerando três mesorregiões: 1) Leste alagoano, compreendendo o Litoral e Mata Atlântica, 2) Sertão alagoano porção Oeste do estado, 3) Agreste, porção transicional entre as mesorregiões do Leste e Sertão alagoanos, conforme estabelecido pelo Instituto Brasileiro de Geografia e Estatística (IBGE). Na obtenção do potencial pedoclimático, as informações do potencial dos solos, obtidos considerando dois níveis tecnológicos para o manejo das terras e das culturas (média tecnologia ou Manejo B, e alta tecnologia ou Manejo C), foram cruzadas com aquelas obtidas para a aptidão climática considerando três cenários pluviométricos: anos chuvosos, anos regulares e anos secos. O cruzamento das informações foi realizado por meio de técnicas de geoprocessamento com o auxílio do software ArcGis, obtendo-se os mapas do potencial pedoclimático. O resultado das interpretações foi organizado em quatro classes de potencial pedoclimático: Preferencial, Médio, Baixo e Muito Baixo. Os resultados indicam que a extensão territorial das classes de potencial pedoclimático apresenta variações importantes em função do nível de manejo adotado e do cenário pluviométrico considerado. Em geral, as áreas com potencial Preferencial estão localizadas nas mesorregiões do Agreste e do Leste Alagoano, onde as condições de solo e de clima são mais favoráveis para o cultivo de milho, com amplitude de 174 km2 a 4.077 km2, o que corresponde a 1% e 15% da área total do estado. Os ambientes com potencial Médio têm ocorrência dispersa nas diferentes regiões do estado, variando de 6.080 km2 a 13.750 km2, compreendendo 25% a 49% da área total, com os maiores valores no manejo com média tecnologia (Manejo B). As áreas que apresentam o potencial Baixo e o Muito Baixo localizam-se, em sua maior parte, na região Oeste do estado, sobretudo no Sertão, onde as limitações de solo e de clima semiárido são mais intensas. Os referidos potenciais também ocorrem na zona úmida costeira, principalmente nos ambientes onde o relevo impõe fortes restrições de uso e manejo do solo e da cultura, independentemente do nível de manejo considerado. Com adoção de alta tecnologia ocorre maior abrangência da classe de potencial pedoclimático Preferencial para a cultura do milho, principalmente na Mesorregião do Agreste, com maior percentual de ocorrência para o cenário pluviométrico regular.bitstream/item/142295/1/BPD-252-Pot-Pedocl-AL-Milho-Alt.pd

Adiabatic and entropy perturbations propagation in a bouncing Universe

By studying some bouncing universe models dominated by a specific class of hydrodynamical fluids, we show that the primordial cosmological perturbations may propagate smoothly through a general relativistic bounce. We also find that the purely adiabatic modes, although almost always fruitfully investigated in all other contexts in cosmology, are meaningless in the bounce or null energy condition (NEC) violation cases since the entropy modes can never be neglected in these situations: the adiabatic modes exhibit a fake divergence that is compensated in the total Bardeen gravitational potential by inclusion of the entropy perturbations.Comment: 25 pages, no figure, LaTe