Dark matter in the $SO(5)\times U(1)$ gauge-Higgs unification

In the $SO(5) \times U(1)$ gauge-Higgs unification the lightest, neutral component of $n_F$ $SO(5)$-spinor fermions (dark fermions), which are relevant for having the observed unstable Higgs boson, becomes the dark matter of the universe. We show that the relic abundance of the dark matter determined by WMAP and Planck data is reproduced, below the bound placed by the direct detection experiment by LUX, by a model with one light and three heavier ($n_F=4$) dark fermions with the lightest one of a mass from 2.3$\,$TeV to 3.1$\,$TeV. The corresponding Aharonov-Bohm phase $\theta_H$ in the fifth dimension ranges from 0.097 to 0.074. The case of $n_F=3$ ($n_F = 5, 6$) dark fermions yields the relic abundance smaller (larger) than the observed limit.