  In Coleman-Weinberg symmetry breaking, all dimensionful parameters vanish and
the symmetry is broken by loop corrections. Before Coleman-Weinberg symmetry
breaking in the Standard Model was experimentally ruled out, it had already
been excluded on cosmological grounds. In this Brief Report, the cosmological
analysis is carried out for Coleman-Weinberg models with extended Higgs
sectors, which are not experimentally ruled out, and general constraints on
such models are given.
