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Register a new userNoncommutative Conformally Coupled Scalar Field Cosmology and its Commutative Counterpart
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Added by
Gustavo Dourado Barbosa
Publication date
2004
fields
Physics
and research's language is
English
Authors
G. D. Barbosa
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We study the implications of a noncommutative geometry of the minisuperspace variables for the FRW universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution in four different scenarios: classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative, the last two employing the Bohmian formalism of quantum trajectories. The role of noncommutativity is discussed by drawing a parallel between its realizations in two possible frameworks for physical interpretation: the NC-frame, where it is manifest in the universe degrees of freedom, and in the C-frame, where it is manifest through theta-dependent terms in the Hamiltonian. As a result of our comparative analysis, we find that noncommutative geometry can remove singularities in the classical context for sufficiently large values of theta. Moreover, under special conditions, the classical noncommutative model can admit bouncing solutions characteristic of the commutative quantum FRW universe. In the quantum context, we find non-singular universe solutions containing bounces or being periodic in the quantum commutative model. When noncommutativity effects are turned on in the quantum scenario, they can introduce significant modifications that change the singular behavior of the universe solutions or that render them dynamical whenever they are static in the commutative case. The effects of noncommutativity are completely specified only when one of the frames for its realization is adopted as the physical one. Non-singular solutions in the NC-frame can be mapped into singular ones in the C-frame.
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We study some consequences of noncommutativity to homogeneous cosmologies by introducing a deformation of the commutation relation between the minisuperspace variables. The investigation is carried out for the Kantowski-Sachs model by means of a comparative study of the universe evolution in four different scenarios: the classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative. The comparison is rendered transparent by the use of the Bohmian formalism of quantum trajectories. As a result of our analysis, we found that noncommutativity can modify significantly the universe evolution, but cannot alter its singular behavior in the classical context. Quantum effects, on the other hand, can originate non-singular periodic universes in both commutative and noncommutative cases. The quantum noncommutative model is shown to present interesting properties, as the capability to give rise to non-trivial dynamics in situations where its commutative counterpart is necessarily static.
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Gravity theory based on current algebra is formulated. The gauge principle rather than the general covariance combined with the equivalence principle plays the pivotal role in the formalism, and the latter principles are derived as a consequence of the theory. In this approach, it turns out that gauging the Poincare algebra is not appropriate but gauging the $SO(N,M)$ algebra gives a consistent theory. This makes it possible to have Anti-de Sitter and de Sitter space-time by adopting a relation between the spin connection and the tetrad field. The Einstein equation is a part of our basic equation for gravity which is written in terms of the spin connection. When this formalism is applied to the $E(11)$ algebra in which the three-form antisymmetric tensor is a part of gravity multiplet, we have a current algebra gravity theory based on M-theory to be applied to cosmology in its classical limit. Without introducing any other ad-hoc field, we can obtain accelerating universe in the manner of the inflating universe at its early stage.
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