Symmetry breaking and conformal coupling with a generalized Higgs potential and the role of the generalized Duffin-Loret equation in the early universe

Abstract

The concepts of spontaneous symmetry breaking and phase transition play an important role in the physics of the early universe and particle theory. In this paper, taken into account the conformal coupling between the scalar field and gravity via the scalar curvature and the complex conjugate of the scalar field, it is shown that spontaneous symmetry breaking can occur in the early universe if the complex scalar field Higgs potential is replaced by a generalized potential consisting of the sum of the Higgs potential and a power law potential of order n . Both higher order and negative values of n were discussed. Some features were raised and the cosmological symmetry breaking in the early universe in an open Robertson-Walker universe was also discussed for different values of n .