Noncommutative quantum cosmology

Pimentel, Luis O.; Mora, César

doi:10.1007/s10714-005-0066-3

Cited by 31 publications

(34 citation statements)

References 10 publications

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“…On the other hand, it is well known that this correspondence, implies changes in the potential term of the WDW equation with a shift in the variables (Compean et al, 2002;Pimentel, 2005), and one possibility for recover (16), and mantaining the old relations to the noncommutative fields, it become…”

Section: Non Commutative Cosmological Quantum Solutionsmentioning

confidence: 99%

“…This deformation is achieved through a Moyal deformation of the Wheeler-DeWitt (WDW) equation, this is similar to noncommutative quantum mechanics (Gamboa, 2001;Chaichian et al, 2001). Some work has been done in this direction, for example in (Barbosa-2005) the authors study the implications of noncommutative geometry in minisuperspace variables for a FRW universe with a conformally coupled scalar field, using the bohmian formalism of quantum trajectories (Barbosa, 2004) also in (Pimentel, 2005) a noncommutative deformation of a scalar field coupled to scalar-tensor type gravity was considered.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the non commutativity is considered between all variables of the minisuperspace (not in its momenta) with three θ i parameters, q i , q j = iθ ij , usually this is made by the Moyal star product ⋆, however, we use one transformation between the non commutative and the commutative variables, resulting in a shifting, and it is well known that this correspondence, implies changes in the potential term of the WDW equation with a shifting in the variables (Compean et al, 2002;Pimentel, 2005). These transformation are not the most general possible to define a noncommutative fields, see for example Carmona et al (Carmona, 2003), where the authors give the generalization the noncommutative harmonic oscillator constructions and shown the most linear transformation between the coordinates and momenta.…”

Section: Introductionmentioning

confidence: 99%

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Noncommutative Bianchi Type II Quantum Cosmology

et al. 2007

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In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler-DeWitt equation for any factor ordering, to the anisotropic Bianchi type II cosmological model are found, using a stiff fluid (γ = 1). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables q i does not commute, so the simplectic structure was modified.

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Section: Non Commutative Cosmological Quantum Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Noncommutative Bianchi Type II Quantum Cosmology

et al. 2007

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“…This was achieved by introducing the Moyal product of functions in the Wheeler-DeWitt equation, in the same manner as is done in noncommutative quantum mechanics. The model analyzed was the Kantowski-Sachs cosmology and was carried out at the quantum level, several works followed with this idea [4,5].…”

Section: Introductionmentioning

confidence: 99%

Effects of deformed phase space on scalar field cosmology

Pérez-Payán¹,

Sabido²,

Yee-Romero³

2013

Phys. Rev. D

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The effects of phase space deformations in standard scalar field cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables to have a deformed Poisson algebra among the coordinates and the canonical momenta. It is found that in the deformed minisuperspace model gives rise to an accelerating scale factor in the absence of a cosmological constant, and this acceleration is a consequence of the phase space deformation parameter β.

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“…In the context of Kantowski-Sachs cosmological model, non-commutativity has been introduced into the classical phase space and classical non-commutative equations of motion have established [57]. For scalar field cosmology, in [58] the classical minisuperspace is deformed and a scalar field is used as the matter component of the universe and the cosmological constant problem and removability of initial curvature singularity is studied in [53]. In [59], the study is focused on the consequences that the non-commutative deformation has on the slow-roll parameter, when an exponential potential for the scalar field is considered.…”

Section: Introductionmentioning

confidence: 99%

Non-singular Brans–Dicke collapse in deformed phase space

et al. 2016

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We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans-Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature [M A Scheel, S L Shapiro & S A Teukolsky, Phys Rev D 51 4236 (1995)], that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.

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Noncommutative quantum cosmology

Cited by 31 publications

References 10 publications

Noncommutative Bianchi Type II Quantum Cosmology

Noncommutative Bianchi Type II Quantum Cosmology

Effects of deformed phase space on scalar field cosmology

Non-singular Brans–Dicke collapse in deformed phase space

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