A Comparison of Quintessence and Non-Linear Born–infeld Scalar Field Using Gold Supernova Data

Liu

Zhang

et al. 2009

Class. Quantum Grav.

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148

By considering the potential parameter Γ as a function of another potential parameter λ [47], We successfully extend the analysis of two-dimensional autonomous dynamical system of quintessence scalar field model to the analysis of three-dimension, which makes us be able to research the critical points of a large number of potentials beyond the exponential potential exactly. We find that there are ten critical points in all, three points P 3,5,6 are general points which are possessed by all quintessence models regardless of the form of potentials and the rest points are closely connected to the concrete potentials. It is quite surprising that, apart from the exponential potential, there are a large number of potentials which can give the scaling solution when the function f (λ)(= Γ(λ) − 1) equals zero for one or some values of λ * and if the parameter λ * also satisfies the condition Eq.(16) or Eq.(17) at the same time. We give the differential equations to derive these potentials V (φ) from f (λ). We also find that, if some conditions are satisfied, the deSitter-like dominant point P 4 and the scaling solution point P 9 ( or P 10 ) can be stable simultaneously but P 9 and P 10 can not be stable simultaneity. Although we survey scaling solutions beyond the exponential potential for ordinary quintessence models in standard general relativity, this method can be applied to other extensively scaling solution models studied in literature [46] including coupled quintessence, (coupled-)phantom scalar field, k-essence and even beyond the general relativity case H 2 ∝ ρ n T . we also discuss the disadvantage of our approach.

Section: Introductionmentioning

confidence: 99%

Exact analysis of scaling and dominant attractors beyond the exponential potential

Liu

Zhang

et al. 2009

Class. Quantum Grav.

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148

Cosmology with non-linear scalar field

Zhang

et al. 2010

Astrophys Space Sci

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Mukhanov and Vikman have studied inflation model with the non-linear (NL) scalar field. We discuss the dark energy model with the Lagrangian in the presence of the square potential. We analyse the sufficient condition for the existence of an attractor solution, and compare the equation of state parameter, the present age of universe and the transition redshift with the quintessence model. We also use the Gold dataset of 157 SN-Ia to finally constrain the parameter of the models. We find that the considered model is consistent with the observation and a little inferior to the quintessence model. The above Lagrangian is similar to the non-linear Born-Infeld (NLBI) scalar field model, while which is superior to the quintessence model.

Exponential Potentials and Attractor Solution of Dilatonic Cosmology

Huang

2007

Int J Theor Phys

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We present the scalar-tensor gravitational theory with an exponential potential in which pauli metric is regarded as the physical space-time metric. We show that it is essentially equivalent to coupled quintessence(CQ) model. However for baryotropic fluid being radiation there are in fact no coupling between dilatonic scalar field and radiation. We present the critical points for baryotropic fluid and investigate the properties of critical points when the baryotropic matter is specified to ordinary matter. It is possible for all the critical points to be attractors as long as the parameters λ and β satisfy certain conditions. To demonstrate the attractor behaviors of these critical points, We numerically plot the phase plane for each critical point. Finally with the bound on β from the observation and the fact that our universe is undergoing an accelerating expansion, we conclude that present accelerating expansion is not the eventual stage of universe. Moreover, we numerically describe the evolution of the density parameters Ω and the decelerating factor q, and computer the present values of some cosmological parameters, which are consistent with current observational data.