ar X iv : h ep - t h / 05 04 03 8 v 1 5 A pr 2 00 5 Quantum and Classical Cosmology With Born - Infeld Scalar Field

A quantum model of gravitation interacting with a Born-Infeld(B-I) type scalar field ϕ is considered. The corresponding Wheeler-Dewitt equation can be solved analytically for both very large and small ˙ ϕ. In the extreme limits of small cosmological scale factor the wave function of the universe can be obtained by applying the methods developed by Vilenkin, Hartle and Hawking. We also suggest that dark energy in the universe might result from the B-I type scalar field with potential and the universe can undergo a phase of accelerating expansion. The corresponding parameter of state equation may lie in the range of −1 < ω < − 1 3. When the potential V (ϕ) = 1 λ , our Lagrangian describes the Chaplygin gas. The parameter of state equation of B-I type scalar field without potential lies in the range of 0 ≤< 1. We find that weak energy and strong energy condition are violated for phantom B-I type scalar field. The parameter of state equation lies in range of ω < −1. We study a specific potential with the form V 0 (1 + ϕ ϕ0)e −(ϕ ϕ 0) in detail and the evolution behavior of the state parameter ω. The attractor property of the system is shown by numerical analysis.