Deviation Of Light Path And Dark Energy Model In Nonlinear Born-Infeld Theory

Nonlinear Born-Infeld theory has won full-grown development since it is firstly proposed by Born and Infeld in order to overcome the inherent problem of classical Maxwell theory in 1934. Especially due to its development in string and D-Brane theory, Nonlinear Born-Infeld theory recovers new emphasis. Its important role in cosmology has been widely studied these years.We considered the deviation of the light path and calculated the deviation valuewasâ–³(?)≈4M/r_min[1-(4M/r_min)³ 9k²Î²/r_min⁶],which would recover the Einstein's result whenβor k equals zero. The second term in the result is so small that can not be detected by current observational apparatus.As a candidate of dark energy, we proposed a Nonlinear Born-Infeld (NLBI) typescalar field model that was described by lagrangian L_NLBI=1/η(1-(?))-u(φ).NLBI scalar field violated the strong energy condition and its state equation w was between -1 and 1, just like the canonical scalar field (i.e. Quintessence). NLBI scalar field can be thought as the sum of dark energy with state equation w=-1 and matter with state equation w=0. Via phase plane and critical point analysis, we get a sufficient condition for an arbitrary potential that admits a later time attractor solution: the potential must have a positive minimum.As to the observational result that state equation w may be less than -1. we proposed the Phantom NLBI scalar field which was described by lagrangianL_PNLBI=1/η(1-(?))-u(φ). This phantom NLBI scalar field violated the weakenergy condition. When the potential is constant, we find that the scale factor has minimum and therefore the universe can avoid the singularity. We find the sufficient condition for the phantom NLBI scalar field that admits a later time attractor solution is the potential must have a positive maximum. In this case, the universe can avoid the "big rip" destiny. We study a specific potential with the form ofu(φ) = u₀(1+φ/φ₀)exp(-φ/φ₀) via phase plane analysis and compute the cosmologicalevolution by numerical analysis in detail. In the presence of radiation and matter, the results show that the phantom field can survive till today(to account for the present observed accelerating expansion) without interfering with the nucleosynthesis of the standard model(the density parameterΩ_φ≈10^-12 at the equipartition epoch), and alsoavoid the future collapse of the universe. This evolution of universe can fit the observation.Due to the important effect of negative potentials on cosmological evolution and its role in cyclic universe, we investigate the NLBI scalar field model with negative potentials, in which the universe undergoes accelerating expansion, decelerating expansion and then contract to singularity. We study some important evolutive epochs and compare them with the Quintessence model. A notable characteristic is that NLBI scalar field behaves as ordinary matter near the singularity while the canonical scalar field behaves as stiff matter. We compare the cosmological evolutions with different potential parameters and find that the value of potential parameters must have an upper bound for anthropic consideration.We study the NLBI scalar field model and the canonical scalar field model with the linear negative potential and the square potential in detail. In the case of same initial conditions and same potential parameters, we find that the age of the universe in NLBI scalar field model is older than the one in canonical scalar field model, and the state parameter w is less than the one in canonical scalar field model. We also use the Gold dataset of 157 SN-Ia to constrain the parameters of the two models. All the results show that the NLBI scalar field is slightly superior to the canonical scalar field model. However, it shows that this superiority is not distinct when the state parameter w approaches -1 and we need compare two models with other observations.We present the Brans-Dicke theory in Einstein frame (EBD) in which Pauli metric is regarded as the physical space-time metric and study the stability of the critical points of the autonomous system. The EBD theory is essentially equivalent to coupled quintessence model. However, the dilatonic scalar field only couples to ordinary matter and does not couple to radiation. We present the stable condition for all critical points and numerically plot the phase plane. We discuss the future destiny of universe using the results of stable condition of critical points and the bound onβfrom the solar-system gravitational experiments.We generalize the NLBI scalar field model and investigate the General Non-canonical Scalar Field Model。We find that a special square potential with a negative minimum is needed to drive the linear field solutionφ=φ₀/, in which theuniverse will undergo accelerating expansion, decelerating expansion, accelerating contraction, decelerating contraction and then collapse to singularity. We find that the linear field solution model is highly degenerate since the cosmic evolutions with any F(X) will be equivalent as long as the first two coefficients ( F₀, F₀) of the seriesexpansion of the function F(X) around X = X. are the same, disregarding the higher order terms of F(X). We give the stable condition for the linear field solution. Westudy the special model where the sound speed diverges and find it is actually one type of the linear field solution model. We analyze the case with a constant barotropic indexγand show that this constantγsolution is only stable forγ₀≤1 . When thepotential is taken to be constant, we obtain the first integral of the field equation and find that in this case the scalar field can be a model unified the dark matter and dark energy.