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

TL;DR

This paper reconstructs the dark energy equation of state within a double complex symmetric gravitational framework, using observational data to explore universe expansion and potential future scenarios like Big Rip.

Contribution

It introduces a novel double complex symmetric gravitational theory to model dark energy and reconstructs its properties from observational data.

Findings

Equation of state remains near -1 at present

EoS transitions from below to above -1 over redshift

Universe's fate could be Big Rip

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 $\omega^{'}(z)$ and $V(\phi)$ for dark energy from real observational data. We find that in the two cases of $J=i,p_J=0$ and $J=\epsilon,p_J\neq 0$, the corresponding equations of state $\omega^{'}(z)$ 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 ($J=\epsilon,p_J\neq 0$). And the fate of the universe would be Big Rip in the future.