The evolution of the universe with the B-I type phantom scalar field

We consider the phantom cosmology with a Lagrangian L = 1/eta [1- root 1 + eta g (mu nu) phi, mu phi, nu] - u(phi) originated from the nonlinear Born-Infeld type scalar field. This cosmological model can explain the accelerating expansion of the universe with the equation of state parameter w <= -1. We get a sufficient condition for an arbitrary potential that admits a late time attractor solution: the value of potential u(X-c) at the critical point (X-c, 0) should be maximum and greater than zero. We study a specific potential with the form of u(phi) = V-0 (1 + phi/phi(0)) e(-phi/phi(0)) via phase plane analysis and compute the cosmological evolution by numerical analysis in detail. The results show that the phantom field survives till today (to account for the present observed accelerating expansion) without interfering with the nucleosynthesis of the standard model (the density parameter Omega(phi) similar or equal to 10(-12) at the equipartition epoch), and also avoid the future collapse of the universe.