M ar 2 00 5 Phantom Cosmology with the Born - Infeld Type Scalar Field

We considered the phantom cosmology with the lagrangian L = 1 η [1 − 1 + ηg µν φ , µ φ , ν ] − u(φ), which is original from the nonlinear Born-Infeld type scalar field with the lagrangian L = 1 η [1 − 1 − ηg µν φ , µ φ , ν ] − u(φ). This cosmological model can explain the accelerated expansion of the universe with the equation of state parameter ω < −1. We find that the potential u(φ) should be greater than 1 η − 1 η √ 1+η ˙ φ 2 for physical permit in our phantom model, and the second derivative of the potential(u ′′ (X c)) should be less than zero at the critical point (X c , 0) if there admits a late time attractor solution. We study a specific potential with the form u(φ) = V 0 (1 + φ φ0)e (− φ φ 0) in detail and show the evolution behavior of the state parameter ω and the phantom field φ via numerical analysis.