The Complex Symmetry Gravitational Theory as a New Alternative of Dark Energy

We propose that complex symmetry gravitational theory (CSGT) explain the accelerating expansion of universe. In this paper universe is taken as the double complex symmetric space. Cosmological solution is obtained within CSGT. The conditions of the accelerating expansion of universe are discussed within CSGT. Moreover, the range of equation of state of matter $\omega_\epsilon$ is given in the hyperbolic imaginary space.