Considering a massive ϕ6 self-interacting scalar field coupled arbitrarily to a (2+1)-dimensional Bianchi type-I spacetime, we evaluate the one-loop effective potential. It is found that ϕ6 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 is also studied. The nature of phase transitions for the present model is clarified to be first order. A first-order phase transition proceeds by nucleation of bubbles of broken phase in the background of unbroken phase.
Renormalization-group improved effective potential for interacting theories with several mass scales in curved spacetime