  I calculate the first corrections to the dynamical pre-exponential factor of
the bubble nucleation rate for a relativistic first-order phase transition in
an expanding cosmological background by estimating the effects of the Hubble
expansion rate on the critical bubbles of Langer's statistical theory of
metastability. I also comment on possible applications and problems that arise
when one considers the field theoretical extensions of these results (the
Coleman-De Luccia and Hawking-Moss instantons and decay rates).
