Bubble-nucleation rates for cosmological phase transitions

We estimate bubble-nucleation rates for cosmological phase transitions. We concentrate on the evaluation of the pre-exponential factor, for which we g ive approximate analytical expressions. Our approach relies on the use of a real coarse-grained potential. We show how the coarse-graining scale can b e determined in the studies of high-temperature phase transitions. We discu ss the metastability bound on the Higgs-boson mass and the electroweak phas e transition. We find that the saddle-point approximation is reliable in th e first case and breaks down in the second case.