Gravitational versus finite-temperature effects in SU(5) symmetry breaking

The influence of classical gravitation in the symmetry breaking of the SU(5) model at early stages of the universe is considered. This is achieved by treating the gravitational field as a c-number external field in the path integral while the remaining particle fields are considered as quantum fields of the unified model. The symmetry breaking of the SU(5) model locally coupled to gravity is described through the effective potential of the quantum field theory, which is renormalized by making use of a zeta-function regularization, and its evolution in the course of the universal time of the treated standard cosmological model is presented. It is shown that the background gravitational field has the tendency to enhance the symmetry breaking that is postulated in the zero-temperature, flat–space-time quantum theory. Although this influence is overcome by the restoration due to the finite-temperature effects through two orders of magnitude in temperature above the mass scale of the SU(5) model, there exists a temperature for which the effective potential develops a strong symmetry breakdown due to the classical gravitational effects. This temperature is between one and two orders of magnitude below the Planck mass scale.