We discuss the cosmological production and the successive evolution of the electroweak monopole in the standard model, and estimate the remnant monopole density at present universe. We con-firm that, although the electroweak phase transition is of the fi-rst order, it is very mildly fi-rst order.
So, the monopole production arises from the thermal fluctuations of the Higgs -field after the phase transition, not the vacuum bubble collisions during the phase transition. Moreover, while the monopoles are produced copiously around the Ginzburg temperature T_G \simeq 59.6 TeV, most of
them are annihilated as soon as created. This annihilation process continues very long, untill the temperature cools down to about 29.5 MeV. As the result the remnant monopole density in the present universe becomes very small, of 10^-􀀀11 of the critical density, too small to a-ect the standard cosmology and too small comprise a major component of dark matter. We discuss the
physical implications of our results on the ongoing monopole detection experiments, in particular on MoEDAL, IceCube, ANTARES, and Auger.