In Coleman-Weinberg symmetry breaking, all dimensionful parameters van
ish and the symmetry is broken by loop corrections. Before Coleman-Wei
nberg symmetry breaking in the standard model was experimentally ruled
out, it had already been excluded on cosmological grounds. In this Br
ief Report, the cosmological analysis is carried out for Coleman-Weinb
erg models with extended Higgs sectors, which are not experimentally r
uled out, and general constraints on such models are given.