Coleman-Weinberg model in Einstein space-time

It is studied radiative symmetry breaking, a la Coleman-Weinberg, in the geometry of a static Einstein universe. It is proved that the symmetric ground state <0,phi,0> = 0, in a nonminimally coupled massless lambdaphi4 theory, can become unstable at high curvature only if 0<or approx., xi approx. lambda<<1. As far as massless scalar QED is concerned, it is found that phase transitions can already occur at low curvature. These conclusions are improved by means of renormalization group techniques