  We provide non-perturbative evidence for the fact that there is no hot
electroweak phase transition at large Higgs masses, $m_H = 95$, 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 GeV $<m_{H,c}<$ 95 GeV and most likely
$m_{H,c} \approx 80$ 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.
