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

Fay, Stéphane; Lehner, Thierry

doi:10.1007/s10714-005-0093-0

Cited by 9 publications

(6 citation statements)

References 23 publications

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“…From previous work [4,5] we are particularly interested in closed models, which are still consistent with observations [6]. The only closed Bianchi type that also allows for FRW subclasses is Bianchi IX, so we shall consider the dynamics of a scalar field in a Bianchi IX model [7,8,9]. Bianchi IX models are known to have very complicated dynamics, exhibiting oscillatory singularities and chaos (mixmaster) [10,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 73%

Anisotropic, nonsingular early universe model leading to a realistic cosmology

2009

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We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a non-singular 'pancaking' solution: the hypersurface volume goes to zero instantaneously at the 'Big Bang', but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the Big Bang. We demonstrate that there exist geodesics extending through the Big Bang, but that there are also incomplete geodesics that spiral infinitely around a topologically closed spatial dimension at the Big Bang, rendering it, at worst, a quasi-regular singularity. The model is thus reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasi-regular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropisation and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by [1,2,3]). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations. We conclude by presenting a separate, bouncing solution, which generalises the known bouncing solution in closed FRW universes.

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Section: Introductionmentioning

confidence: 73%

Anisotropic, nonsingular early universe model leading to a realistic cosmology

2009

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“…For a discussion of the chaotic behavior inherent the homogeneous early cosmologies, see [101,236,103,444,197,65,256,477,147,171,66,479,155,134,320,159,68,475,175,120,476,457,4,350,153,356,180,125,194,284,468].…”

Section: )mentioning

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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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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“…The latter has naturally been examined in cosmological solutions, mainly in Bianchi IX (Mixmaster) models. While the secular debate about chaoticity and the very nature of these universes continues (Coley 2002; Fay & Lehner 2004; Benini & Montani 2004; Soares & Stuchi 2005; Heinzle, Röhr & Uggla 2006; Buzzi, Llibre & da Silva 2007; Andriopoulos & Leach 2008; Heinzle & Uggla 2009), one of the later attractors is to assess the effect of the cosmological constant and/versus that of a scalar field within the Friedmann–Lematre–Robertson–Walker model dynamics (Jorás & Stuchi 2003; Faraoni, Jensen & Theuerkauf 2006; Hrycyna & Szydłowski 2006; Lukes‐Gerakopoulos, Basilakos & Contopoulos 2008; Maciejewski et al 2008). [We only give several more recent references here.…”

Section: Introductionmentioning

confidence: 99%

Free motion around black holes with discs or rings: between integrability and chaos - I

Semerák¹,

Suková²

2010

Monthly Notices of the Royal Astronomical Society

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Geodesic dynamics is regular in the fields of isolated stationary black holes. However, due to the presence of unstable periodic orbits, it easily becomes chaotic under various perturbations. Here, we examine what amount of stochasticity is induced in Schwarzschild space–time by the presence of an additional source. Following astrophysical motivation, we specifically consider thin rings or discs lying symmetrically around the hole, and describe the total field in terms of exact static and axially symmetric solutions of Einstein's equations. The growth of chaos in time‐like geodesic motion is illustrated on Poincaré sections, on time series of position or velocity and their Fourier spectra, and on time evolution of the orbital ‘latitudinal action’. The results are discussed in terms of dependence on the mass and position of the ring/disc and on geodesic parameters (energy and angular momentum). In the Introduction, we also add an overview of the literature.

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

Cited by 9 publications

References 23 publications

Anisotropic, nonsingular early universe model leading to a realistic cosmology

Anisotropic, nonsingular early universe model leading to a realistic cosmology

Classical and Quantum Features of the Mixmaster Singularity

Free motion around black holes with discs or rings: between integrability and chaos - I

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