$E_6$ unification in a model of dark energy and dark matter

A model of dark energy and dark matter was proposed earlier by one of us (PQH) which involved an unbroken gauge group $SU(2)_Z$ whose coupling $\alpha_Z \equiv g_Z^2/4 \pi\sim O(1)$ at a scale $\Lambda_Z \sim 3 \times 10^{-3} eV$ starting from a value within the range of the Standard Model (SM) couplings at a high energy scale $\sim 10^{16} GeV$. In that model, the universe is assumed to be presently trapped in a false vacuum with an energy density $\sim \Lambda_Z^4$. In this paper, we present a scenario in which $SU(2)_Z$ is unified with the SM through several steps: $E_6 \to SU(2)_Z \otimes SU(6) \to SU(2)_Z \otimes SU(3)_c \otimes SU(3)_L \otimes U(1) \to SU(2)_Z \otimes SU(3)_c \otimes SU(2)_L \otimes U(1)_Y$. This unification provides a rationale for why the value of the $SU(2)_Z$ coupling is within the range of the SM couplings at high energies. The particle content and the route of symmetry breaking in this model is very different from the usual $E_6$ unification encountered in the literature. Several implications, in addition to the dark energy, include the existence of heavy mirror particles which could be searched for at future colliders such as the LHC.