Thermal and Curvature Effects to Spontaneous Symmetry Breaking in phi⁴ Theory

We study the thermal and curvature effect to spontaneous symmetry breaking in phi^4 theory. The effective potential is evaluated in D-dimensional static universe with positive curvature R X S^{D-1} or negative curvature R X H^{D-1}. It is shown that temperature and positive curvature suppress the symmetry breaking, while negative curvature enhances it. To consider the back-reaction we numerically solve the gap equation and the Einstein equation simultaneously. The solution gives the relationship between the temperature and the scale factor.