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Hamilton (Jacobi) formulation of the dark sector of the universe and contextualized studies on quantum cosmology and non-commutativity

Grant number: 12/03561-0
Support type:Scholarships abroad - Research
Effective date (Start): September 01, 2012
Effective date (End): August 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Astronomy
Principal Investigator:Alex Eduardo de Bernardini
Grantee:Alex Eduardo de Bernardini
Host: Orfeu Bertolami Neto
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Local de pesquisa : Universidade do Porto (UP), Portugal  

Abstract

At first analysis, we introduce a generalized procedure for the Hamilton(Jacobi) formulation for field prescriptions (scalar, tachyonic, Thomas-Fermi, generalized Born-Infeld, etc.) of the fluid corresponding to the dark sector of the universe when it is eventually coupled to a generalized element the cosmic inventory (baryons, neutrinos and radiation) parametrized by an isentropic fluid. In particular, we intend to apply such a formulation in the context of the GCG model.In particular, it corresponds to a class of models derived from a generalized model of D-branes which, starting from a Lagrangian approximated by a Thomas-Fermi Lagrangian leads to a representation in the form of a generalized Lagrangian of Born-Infeld.In this case, the dynamics would be described in terms of generalized tachyonic fields. The application of the generalized form of this formalism allows us to investigate some variations for descriptions of the dark sector according to the Thomas-Fermi Lagrangian as well as to the generalized Born-Infeld Lagrangian, for which a duality can be established. At first, we consider a universe with the cosmic inventory consisting of an isentropic fluid and a general element of the dark sector described by a generic Lagrangian field. Our preliminary studies indicate that it is always possible to establish a descriptive duality with a real scalar field prescription. Thus, by formulating the problem through the Hamilton-Jacobi procedure, whatever the Lagrangian, one can get a first-order formulation for the study of fields and potentials through which can determine the dynamics of the dark sector of the universe. Dealing with problems related to this formalism, not necessarily restricted to the Chaplygin gas scenario, we can determine the conditions for the formation of lump structures, the immediate consequences on the stability of the propagation of perturbations, and the outlines of the (slow-roll) conditions of the inflationary model. In parallel, we shall investigate extensions of quantum mechanics in the non-commutative phase space and its applications in the formulation of quantum field cosmology, where non-commutativity may be relevant to the selection of possible initial states of the universe. In general, we assume the non-commutativity of space-time as an inherent feature of quantum gravity, so that its effects would be relevant only at energies of the order of those of the early universe. It is then possible to investigate the role of non-commutative geometry in the context of quantum cosmology, in particular, as an extension of noncommutative quantum mechanics. Part of the recent literature regarding the description of the early universe, and its correspondence with the dark sector, involves results from numerical solutions of the equation of Wheeler-De Witt. We intend to investigate if, somehow, the problem in the space of commutative variables (which maps the space non-commutative variables according to a Seiberg-Witten map), allows for some simplified approach according to the Hamiltonian formulation, through the same way that we have proceeded the universe of FRW, safeguarding, of course, the specifications of the AMD metrics. (AU)

Scientific publications (7)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BASTOS, CATARINA; BERNARDINI, ALEX E.; BERTOLAMI, ORFEU; DIAS, NUNO COSTA; PRATA, JOAO NUNO. Robertson-Schrodinger-type formulation of Ozawa's noise-disturbance uncertainty principle. Physical Review A, v. 89, n. 4 APR 22 2014. Web of Science Citations: 18.
BERNARDINI, A. E.; BERTOLAMI, O. The Hamiltonian formalism for scalar fields coupled to gravity in a cosmological background. ANNALS OF PHYSICS, v. 338, p. 1-20, NOV 2013. Web of Science Citations: 5.
BASTOS, CATARINA; BERNARDINI, ALEX E.; BERTOLAMI, ORFEU; DIAS, NUNO COSTA; PRATA, JOAO NUNO. Entanglement due to noncommutativity in phase space. Physical Review D, v. 88, n. 8 OCT 10 2013. Web of Science Citations: 19.
BERNARDINI, A. E.; BERTOLAMI, O. Equivalence between Born-Infeld tachyon and effective real scalar field theories for brane structures in warped geometry. Physics Letters B, v. 726, n. 1-3, p. 512-517, OCT 2013. Web of Science Citations: 16.
BERNARDINI, A. E. Cosmological neutrino entropy changes due to flavor statistical mixing. EPL, v. 103, n. 3 AUG 2013. Web of Science Citations: 1.
BERNARDINI, A. E.; BERTOLAMI, O. Probing phase-space noncommutativity through quantum beating, missing information, and the thermodynamic limit. Physical Review A, v. 88, n. 1 JUL 1 2013. Web of Science Citations: 25.
RODRIGUES, M. G.; BERNARDINI, A. E. ACCRETION OF NONMINIMALLY COUPLED GENERALIZED CHAPLYGIN GAS INTO BLACK HOLES. INTERNATIONAL JOURNAL OF MODERN PHYSICS D, v. 21, n. 9 SEP 2012. Web of Science Citations: 5.

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