ar X iv : h ep - t h / 06 10 18 8 v 1 1 7 O ct 2 00 6 Cosmologies with General Non - Linear Scalar Field

We generally investigate a new class of scalar field model with the lagrangian L = F (X) − V (φ). We find that it is the square potential(with a negative minimum) drives the usual linear field solution while in K-essence model the potential should be taken as a inverse square form. The linear field solution model is isomorphic with a special model where its sound speed diverges. We find that our model with a constant potential is actually equivalent to the K-essence model also with a constant potential. With a simple form of F (X) we indicate that our model can be also considered as a unified model of dark matter and dark energy. Finally we study the case when the baryotropic index γ is constant. It shows that, unlike the K-essence, the detailed form of F (X) depends on the potential. When the potential is constant We find the exact solution for F (X).