Coleman Weinberg model in Einstein spacetime

We study radiative symmetry breaking, a la Coleman-Weinberg, in the geometry of a static Einstein Universe. We prove that the symmetric ground state <0|phi|0>=0, in a non-minimally coupled massless lambda phi4 theory, can become unstable at high curvature only if 0<=xi approx.= lambda<<1. As far as massless scalar QED is concerned, we find that phase transitions can already occur at low curvature. These conclusions are improved by means of Renormalization Group techniques. (author)