  We study the electroweak phase transition and the critical bubble in the
scale-invariant two Higgs doublet model taking the recent LHC data into
account. The sphaleron energy in this model is evaluated for the first time. It
is found that the strong first-order electroweak phase transition is the
inevitable consequence to be consistent with the observed 125 GeV Higgs boson.
In such a case, the signal strength of the Higgs decay to two gammas and the
triple Higgs boson coupling could deviate from the SM values by $-10$% and
$+82$%, respectively.
