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

Fay, Stéphane

doi:10.1007/s10714-005-0107-y

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…For a discussion of the Bianchi I model in presence of several matter sources, see the following literature [390,265,451,442,121,388,2,366,210,422,127,270,30,360,364,78,232,365,358,363,463,133,423,321,126,28,490,286,123,288,352,372,193,452,414,249,136,453,119].…”

Section: The Role Of Mattermentioning

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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Section: The Role Of Mattermentioning

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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“…Given its importance for studying the possible effects of an anisotropy in the early universe on presentday observations, many researchers have investigated the BI model from different perspectives. Examples of these studies are, string theory (Alexeyev et al 2001;Rao et al 2008;Rathore & Mandawat 2009;Bali & Gupta 2010;Rikhvitsky et al 2012), dynamical properties (Salucci & Fabbri 1983;Chimento & Forte 2006;Ellis 2006;Akarsu & Kılınç 2010a,b;Adhav et al 2011;Singh & Chaubey 2012;Appleby & Linder 2012;Mostafapoor & Grøn 2013;Pradhan et al 2013;Singh & Chaubey 2013;Ali & Rahaman 2013;Kohli & Haslam 2013), the singularity problem (Bronnikov et al 2004;Khalatnikov et al 2003;Belinskij et al 1970), the spinor/scalar field (Saha 2001a,b;Fay 2005;Saha & Boyadjiev 2004;Saha 2005Saha , 2006Kucukakca et al 2012;Pradhan et al 2012;Saha 2013;Carloni et al 2013) and perturbations in the early phase of inflation (Gümrükçüoglu & Peloso 2007;Pereira et al 2007;Dong 2010;Bali 2011;Aluri & Jain 2012;Kofman et al 2011). Separately, Maartens et al (1995b) obtain evolution equations by which matter imposes anisotropies on freely propagating CMB radiation, leading to a new model independent way of using anisotropy measurements to limit the deviations of the Universe from a FRW geometry.…”

Section: Introductionmentioning

confidence: 99%

Bianchi I model: an alternative way to model the present-day Universe

Russell

Kilinç

Pashaev

2014

Monthly Notices of the Royal Astronomical Society

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Although the new era of high precision cosmology of the cosmic microwave background (CMB) radiation improves our knowledge to understand the infant as well as the presentday Universe, it also leads us to question the main assumption of the exact isotropy of the CMB. There are two pieces of observational evidence demonstrating that there is no exact isotropy. These are first the existence of small anisotropy deviations from isotropy of the CMB radiation and second, the presence of large angle anomalies that are shown as real features by the Planck satellite results. These evidences are particularly important since isotropy is one of the two main postulates of the Copernican principle on which the FRW models are built. This almost isotropic CMB radiation implies that the universe is almost a FRW universe, as is proved by previous studies.Assuming the matter component forms the deviations from isotropy in the CMB density fluctuations when matter and radiation decouples, we here attempt to find possible constraints on these deviations by using the Bianchi type I (BI) anisotropic model which is asymptotically equivalent to the standard FRW. Then we obtain the separations from the FRW type scale factor and the Hubble parameter in the form of time dependent functions. Hence we put constraints on the anisotropy coefficients from the anisotropy upper limits of the recent Planck data and from the theoretical consistency relation. These constraints lead us to obtain a BI model which becomes to be an almost FRW in time that is consistent with observational data of the CMB.

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Energy exchange for homogeneous and isotropic universes with a scalar field coupled to matter

Giambò

Miritzis

2010

Class. Quantum Grav.

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We study the late time evolution of flat and negatively curved Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source and a scalar field arising in the conformal frame of f (R) theories nonminimally coupled to matter. Under mild assumptions on the potential V we prove that equilibria corresponding to non-negative local minima for V are asymptotically stable, as well as horizontal asymptotes approached from above by V . We classify all cases of the flat model where one of the matter components eventually dominates. In particular for a nondegenerate minimum of the potential with zero critical value we prove in detail that if γ, the parameter of the equation of state is larger than one, then there is a transfer of energy from the fluid to the scalar field and the later eventually dominates in a generic way.

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

Cited by 5 publications

References 20 publications

Classical and Quantum Features of the Mixmaster Singularity

Classical and Quantum Features of the Mixmaster Singularity

Bianchi I model: an alternative way to model the present-day Universe

Energy exchange for homogeneous and isotropic universes with a scalar field coupled to matter

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