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Electroweak theory is extended to $SU_L(2)\times U_Y(1)\times U_{\phi}(1)$,where $U_{\phi}(1)$ comes from the coupling of inflaton field to Higgs field.There arises an extremely light boson, $Y_{\mu}$. We resemble it as thewavelike dark matter, $\Psi$DM, through the dynamical analysis. Theinteractions of $Y_{\mu}$ may provide an explanation for the Bullet Clusterobservations. Besides, a possible mechanism to produce $Y_{\mu}$ is discussed.

$\Psi$DM and the Bullet Cluster: Couple Inflaton to Higgs Field