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Ureña‐López, L. Alfonso; Rodríguez, Manuel de Buenaga; Gómez, José María

doi:10.1023/a:1002632712378

Cited by 39 publications

(29 citation statements)

References 19 publications

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“…These very simple tools give us the possibility to correlate such important concepts in the phase space like past and future attractors (also saddle equilibrium points), limit cycles, heteroclinic orbits, etc., with generic behavior of the dynamical system derived from the set of equations (6), without the need to analytically solve them. A very compact and basic introduction to the application of the dynamical systems in cosmological settings with scalar fields can be found in the references [19][20][21][22][23][24].…”

Section: Basic Setupmentioning

confidence: 99%

Brans-Dicke cosmology does not have theΛCDMphase as a universal attractor

2015

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In this paper we seek for relevant information on the asymptotic cosmological dynamics of the Brans-Dicke theory of gravity for several self-interaction potentials. By means of the simplest tools of the dynamical systems theory, it is shown that the general relativity de Sitter solution is an attractor of the Jordan frame (dilatonic) Brans-Dicke theory only for the exponential potential U (ϕ) ∝ exp ϕ, which corresponds to the quadratic potential V (φ) ∝ φ 2 in terms of the original Brans-Dicke field φ = exp ϕ, or for potentials which asymptote to exp ϕ. At the stable de Sitter critical point, as well as at the stiff-matter equilibrium configurations, the dilaton is necessarily massless. We find bounds on the Brans-Dicke coupling constant ωbd, which are consistent with well-known results.

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Section: Basic Setupmentioning

confidence: 99%

Brans-Dicke cosmology does not have theΛCDMphase as a universal attractor

2015

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“…This will be achieved through the use of the tools of dynamical systems (for some pedagogical presentations, see Ref. [7]), together with appropriate changes of variables that are more than suitable to exploit the intrinsic symmetries of the equations of motion. Even though we will be mainly concerned with single-field models of inflation, the techniques that will be developed here have been recently extended to different cosmological settings with scalar fields [8].…”

Section: Introductionmentioning

confidence: 99%

New perturbative method for analytical solutions in single-field models of inflation

Ureña–López

2016

Phys. Rev. D

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We propose a new parametrization of the background equations of motion corresponding to (canonical) single-field models of inflation, which allows a better understanding of the general properties of the solutions and of the corresponding predictions in the inflationary observables. Based on the tools of dynamical systems, the method suggests that inflation comes in two flavors: power-law and de Sitter. Power-law inflation seems to occur for a restricted type of potentials, whereas de Sitter inflation has a much broader applicability. We also show a general perturbative method, by means of series expansion, to solve the new equations of motion around the critical point of the de Sitter type, and how the method can be used for arbitrary models of de Sitter inflation. It is then argued that for the latter there are two general classes of inflationary solutions, given in terms of the behavior of the tensor-to-scalar ratio as a function of the number N of e-folds before the end of inflation: r ∼ N −1 (Class I), or r ∼ N −2 (Class II). We give some examples of the two classes in terms of known scalar field potentials, and compare their general predictions with constraints obtained from observations.

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“…To analyze the fixed point for arbitrary potentials, we have used the method called in our notation h-devisers, which allows us to perform the whole analysis for a wide range of potentials [95][96][97][98][99][100][101][102][103][104][105][106]. Using this method, we have studied the exponential potential and non-exponential potentials for which h(λ) can be written in an explicit form, e.g, V (φ) = V 0 e −σφ + V 1 , σ = 0, h ≡ −λ(λ − σ); V (φ) = (µφ) k k with h ≡ − λ 2 k ; V (φ) = V 0 (cosh(ξφ) − 1), ξ = 0, with h ≡ − 1 2 λ 2 − ξ 2 ; V B (φ) = V 1 e −3(wm+1)φ + V 2 e −6wmφ , with h B ≡ − (λ − 3(w m + 1)) (λ − 6w m ) , and V C (φ) = V 1 e −3(1+wm)φ + V 2 e − 3 2 (3+wm) , with h C ≡ − 1 2 (λ − 3(w m + 1)) (2λ − 3(3 + w m )).…”

Section: Discussionmentioning

confidence: 99%

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

et al. 2018

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In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization. 95.35.+d, 95.36.+x 1 In the following, with the term "canonical" scalar field we refer to the quintessence scalar field with a canonical kinetic term, that is, with Lagrangian L φ = K − V .

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Cited by 39 publications

References 19 publications

Brans-Dicke cosmology does not have theΛCDMphase as a universal attractor

Brans-Dicke cosmology does not have theΛCDMphase as a universal attractor

New perturbative method for analytical solutions in single-field models of inflation

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

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