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

Abstract

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 ${\cal M}^4_C(J)$ which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann Equations but also the two constraint conditions $p_J=0$ and $J^2=1$ are obtained. Furthermore, using parametric $D_L(z)$ ansatz, we reconstruct the $ω^{'}(z)$ and $V(ϕ)$ for dark energy from real observational data. We find that in the two cases of $J=i,p_J=0$ and $J=ε,p_J\neq 0$, 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 ${\cal M}^4_C(J)$, may be either ordinary complex ($J=i,p_J=0$) or hyperbolic complex ($J=ε,p_J\neq 0$). And the fate of the universe would be Big Rip in the future.