  Condsidering a massive self-interacting phi ^6 scalar field coupled
arbitrarily to a (2+1) dimensional Bianchi type-I spacetime, we evaluate the
one-loop effective potential. It is found that phi ^6 potential can be
regularized in (2+1) dimensional curved spacetime. A finite expression for the
energy-momentum tensor is obtained for this model. Evaluating the finite
temperature effective potential, the temperature dependence of phase
transitions is studied. The crucial dependence of the phase transitions on the
spacetime curvature and on the coupling to gravity are also verified. We also
discuss the nucleation of bubbles in a phi ^6 model. It is found that there
exists an exact solution for the damped motion of the bubble in the thin wall
regime.
