SO(1,1) dark energy model and the universe transition

We suggest a scalar model of dark energy with the SO(1,1) symmetry. The model may be reformulated in terms of a real scalar field $\mathrm{\Phi }$ and the scale factor $a$ so that the Lagrangian may be decomposed as that of the real quintessence model plus the negative coupling energy term of $\mathrm{\Phi }$ to $a$. The existence of the coupling term $L^c$ leads to a wider range of $w_{\mathrm{\Phi }}$ and overcomes the problem of negative kinetic energy in the phantom universe model. We propose a power-law expansion model of univese with time-dependent power, which can describe the phantom universe and the universe transition from ordinary acceleration to super acceleration.