Cosmologies with General Non-Canonical Scalar Field

We generally investigate the scalar field model with the lagrangian $L=F(X)-V(ϕ)$, which we call it {\it General Non-Canonical Scalar Field Model}. We find that it is a special square potential(with a negative minimum) that drives the linear field solution($ϕ=ϕ_0t$) while in K-essence model(with the lagrangian $L=-V(ϕ)F(X)$) the potential should be taken as an inverse square form. Hence their cosmological evolution are totally different. We further find that this linear field solutions are highly degenerate, and their cosmological evolutions are actually equivalent to the divergent model where its sound speed diverges. We also study the stability of the linear field solution. With a simple form of $F(X)=1-\sqrt{1-2X}$ we indicate that our model may be 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 $V(ϕ)$. We analyze the stability of this constant $γ_0$ solution and find that they are stable for $γ_0\leq1$. Finally we simply consider the constant c_s^2 case and get an exact solution for F(X)

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