Reconstructing Equation of State for Dark Energy in Double Complex Symmetric Gravitational Theory

We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory （DCSGT）. The universe we live in is taken as the real part of the whole spacetime MC^4（J）, which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann equations but also the two constraint conditions py = 0 and J^2 = 1 are obtained. Farthermore, using parametric DL（z） ansatz, we reconstruct the ω/（z） and V（Ф） for dark energy from real observational data. We find that in the two cases of J = i, pJ = 0, and J = ε, pJ≠0, the corresponding equations of state ω＇（z） remain close to -1 at present （z = 0） and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime MC^4（J）, may be either ordinary complex （J = i, pJ = 0） or hyperbolic complex （J = ε, pJ≠ 0）. And the fate of the universe would be Big Rip in the future.