Is There a Hot Electroweak Phase Transition atmH≳mW?

We provide nonperturbative evidence for the fact that there is no hot first or second order electroweak phase transition at large Higgs masses, $m_H=95\mathrm{}$, 120, and 180 GeV. This means that the line of first order phase transitions separating the symmetric and broken phases at small $m_H$ has an end point $m_{H,c}$. In the minimal standard electroweak theory $70<\mathrm{}{m}_{H,c}<95\mathrm{}\mathrm{GeV}$ and most likely $m_{H,c}\approx 80\mathrm{GeV}$. If the electroweak theory is weakly coupled and the Higgs boson is found to be heavier than the critical value (which depends on the theory in question), cosmological remnants from the electroweak epoch are improbable.