Thermal and curvature effects on spontaneous symmetry breaking in 4 theory

We study the thermal and curvature effects on spontaneous symmetry breaking in Φ 4 theory. The effective potential is evaluated in the D-dimensional static universe with positive curvature R ⊗ S D-1 or negative curvature R ⊗ 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.