Analysis of Coleman-Weinberg potentials in orbit space: General method and application to the inflationary universe

We present a general method to analyze Coleman-Weinberg potentials in the orbit space, which is applicable to any irreducible representation. As an example, the structure of the SU(5) Coleman-Weinberg potential with scalars assigned to the adjoint representation is analyzed in complete detail, which confirms the general conclusion reached by Breit, Gupta and Zaks, and Moss that the phase transition in the new inflationary scenario of the early universe is problematic. We show that the disease found in the SU(5) case is common to all SU(N) (N>3) and SO(2N) (Nnot=4,8) adjoints, and that the adjoints of SO(8) and exceptional groups are immune from the disease. (orig.)