Isotropization of Bianchi class A models with a minimally coupled scalar field and a perfect fluid

Fay, Stéphane

doi:10.1088/0264-9381/21/6/020

Cited by 8 publications

(5 citation statements)

References 29 publications

(62 reference statements)

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“…The matrix β ab satisfies the condition Trβ = 0, ensuring hypersurface threevolume dependance on the conformal factor α only as V Univ ∼ R 3 0 e 3α [370]. For a review of works devoted to the study of the dynamics of Bianchi models in different cosmological paradigms see the collection of articles [391,421,200,441,116,348,483,144,41,500,430,429,428,345,492,25,143,346,122,255,306,157,426,397,458,445,107,313,395,396,356,137,309,207,311,192,142,260,353,184,113,488,496,454,10,13,…”

Section: 7)mentioning

confidence: 99%

“…Therefore we are interested to investigate some mechanisms allowing a transition between these two cosmological epochs. When the anisotropy of the Universe is sufficiently suppressed, we can speak of a quasi-isotropization of the model [472,139,140,146] (for a detailed discussion of the isotropization mechanism see [183,182,460,366,191,232,47,271,233,126,504,114,499,115,192,282,113,359,413]) and such mechanism can be regarded as a "bridge" between the two stages.…”

Section: Isotropization Mechanismsmentioning

confidence: 99%

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Classical and Quantum Features of the Mixmaster Singularity

Montani

Battisti

Benini

et al. 2008

Int. J. Mod. Phys. A

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This review article is devoted to analyze the main properties characterizing the cosmological singularity associated to the homogeneous and inhomogeneous Mixmaster model. After the introduction of the main tools required to treat the cosmological issue, we review in details the main results got along the last forty years on the Mixmaster topic. We firstly assess the classical picture of the homogeneous chaotic cosmologies and, after a presentation of the canonical method for the quantization, we develop the quantum Mixmaster behavior. Finally, we extend both the classical and quantum features to the fully inhomogeneous case. Our survey analyzes the fundamental framework of the Mixmaster picture and completes it by accounting for recent and peculiar outstanding results.are obtained requiring the action for the matter S m introduced in Eq. (2.1.11) to be invariant under diffeomorphisms. For the Einstein equations, the Bianchi identities ∇ i G ij = 0 may be viewed as a consequence of the invariance of the Hilbert action under diffeomorphisms. Let us now list the principal aspects of the three fields under consideration.• The energy-momentum tensor of a perfect fluid is given bywhere u i is a unit time-like vector field representing the four-velocity of the fluid. The scalar functions p and ρ are the energy density and the pressure, respectively, as2.8b) where j k is the current density four-vector of electric charge and [ ] denote the antisymmetric sum, or in the forms language equations (2.2.8) are written as d ⋆ F = 4π ⋆ j (2.2.9a) dF = 0 (2.2.9b)where d is the exterior derivative and ⋆ is the Hodge star operator [505,370].

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Section: 7)mentioning

confidence: 99%

Section: Isotropization Mechanismsmentioning

confidence: 99%

Classical and Quantum Features of the Mixmaster Singularity

Montani

Battisti

Benini

et al. 2008

Int. J. Mod. Phys. A

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“…In other words, we will assume that all these quantities tend sufficiently quickly to their equilibrium values. We have discussed these two assumptions in [16]. We reproduce below the discussion of this last paper.…”

Section: Assumptions For the Stability Of Our Resultsmentioning

confidence: 99%

Isotropisation of flat homogeneous Bianchi type I model with a non minimally coupled and massive scalar field

Fay

2005

Gen Relativ Gravit

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“…It is explained in part by calculating the necessary condition such that the Universe becomes isotropic and expanding. Using [22], it writes ω < 1 2 (k 2 −3) and is valid when 3+2ω and U are positive. It is the equation of an hyperbole in the (ω, k) plane with a minimum in (ω, k) = (−3/2, 0) in agreement with the figure 4.…”

Section: Power Law Of the Scalar Fieldmentioning

confidence: 99%

Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back

Fay

Lehner

2005

Gen Relativ Gravit

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We use numerical integrations to study the asymptotical behaviour of a homogeneous but anisotropic Bianchi type IX model in General Relativity with a massive scalar field. As it is well known, for a Brans-Dicke theory, the asymptotical behaviour of the metric functions is ruled only by the BransDicke coupling constant ω 0 with respect to the value −3/2. In this paper we examine if such a condition still exists with a massive scalar field. We also show that, contrary to what occurs for a massless scalar field, the singularity oscillatory approach may exist in presence of a massive scalar field having a positive energy density.

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Isotropization of Bianchi class A models with a minimally coupled scalar field and a perfect fluid

Cited by 8 publications

References 29 publications

Classical and Quantum Features of the Mixmaster Singularity

Classical and Quantum Features of the Mixmaster Singularity

Isotropisation of flat homogeneous Bianchi type I model with a non minimally coupled and massive scalar field

Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back

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