Thermal and Curvature Effects to Spontaneous Symmetry Breaking in phi^4   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. 
T. Hattori, M. Hayashi, T. Inagaki and Y. Kitadono