Non-minimally coupled scalar field cosmology on the phase plane

Hrycyna, Orest; Szydłowski, Marek

doi:10.1088/1475-7516/2009/04/026

Cited by 51 publications

(40 citation statements)

References 36 publications

(66 reference statements)

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“…We can treat the dynamical system (86)-(87) as a sewn dynamical system [47,48]. In this case, we divide the phase portrait into two parts: the first part is for a < a sing and the second part is for a > a sing .…”

Section: Singularities In the Starobinsky Model In The Palatini Formamentioning

confidence: 99%

Starobinsky cosmological model in Palatini formalism

Stachowski

Szydłowski

Borowiec³

2017

Eur. Phys. J. C

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We classify singularities in FRW cosmologies, which dynamics can be reduced to the dynamical system of the Newtonian type. This classification is performed in terms of the geometry of a potential function if it has poles. At the sewn singularity, which is of a finite scale factor type, the singularity in the past meets the singularity in the future. We show that such singularities appear in the Starobinsky model in f (R) =R + γR 2 in the Palatini formalism, when dynamics is determined by the corresponding piecewise-smooth dynamical system. As an effect we obtain a degenerate singularity. Analytical calculations are given for the cosmological model with matter and the cosmological constant. The dynamics of model is also studied using dynamical system methods. From the phase portraits we find generic evolutionary scenarios of the evolution of the universe. For this model, the best fit value of γ = 3γ H 2 0 is equal 9.70 × 10 −11 . We consider a model in both Jordan and Einstein frames. We show that after transition to the Einstein frame we obtain both the form of the potential of the scalar field and the decaying Lambda term.

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Section: Singularities In the Starobinsky Model In The Palatini Formamentioning

confidence: 99%

Starobinsky cosmological model in Palatini formalism

Stachowski

Szydłowski

Borowiec³

2017

Eur. Phys. J. C

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“…It would be useful to look at the dynamical problem from the point of view of sewn dynamical systems [44,45]. Our strategy is as follows.…”

Section: Phase Portrait From a Potentialmentioning

confidence: 99%

Do sewn up singularities falsify the Palatini cosmology?

et al. 2016

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We investigate further (cf. Borowiec et al. JCAP 1601(01):040, 2016) the Starobinsky cosmological model R + γ R 2 in the Palatini formalism with a Chaplygin gas and baryonic matter as a source in the context of singularities. The dynamics reduces to the 2D sewn dynamical system of a Newtonian type (a piece-wise-smooth dynamical system). We demonstrate that the presence of a sewn up freeze singularity (glued freeze type singularities) for the positive γ is, in this case, a generic feature of the early evolution of the universe. It is demonstrated that γ equal zero is a bifurcation parameter and the dynamics qualitatively changes as the γ sign is changing. On the other side for the case of negative γ instead of the big bang the sudden bounce singularity of a finite scale factor does appear and there is a generic class of bouncing solutions. While the γ > 0 is favored by data only very small values of γ parameter are allowed if we require agreement with the CDM model. From the statistical analysis of astronomical observations, we deduce that the case of only very small negative values of γ cannot be rejected. Therefore, observation data favor the universe without the ghost states ( f (R) > 0) and tachyons ( f (R) > 0).

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“…Many authors have studied models with a scalar field nonminimally coupled to gravity in the framework of GR [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Recently, it has been considered, in analogy with a similar construction in GR, a nonminimally coupled scalar field in the context of TG by adding a term f (φ) T , with f (φ) a function of the scalar field and T the so-called torsion scalar.…”

Section: Introductionmentioning

confidence: 99%

A novel teleparallel dark energy model

Otalora

2016

Int. J. Mod. Phys. D

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Abstract. Although equivalent to general relativity, teleparallel gravity is conceptually speaking a completely different theory. In this theory, the gravitational field is described by torsion, not by curvature. By working in this context, a new model is proposed in which the four-derivative of a canonical scalar field representing dark energy is nonminimally coupled to the "vector torsion". This type of coupling is motivated by the fact that a scalar field couples to torsion through its fourderivative, which is consistent with local spacetime kinematics regulated by the de Sitter group SO(1, 4). It is found that the current state of accelerated expansion of the Universe corresponds to a late-time attractor that can be (i) a dark-energy-dominated de Sitter solution (ω φ = −1), (ii) a quintessence-type solution with ω φ ≥ −1, or (iii) a phantom-type ω φ < −1 dark energy.

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Non-minimally coupled scalar field cosmology on the phase plane

Cited by 51 publications

References 36 publications

Starobinsky cosmological model in Palatini formalism

Starobinsky cosmological model in Palatini formalism

Do sewn up singularities falsify the Palatini cosmology?

A novel teleparallel dark energy model

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