Real effective potentials for phase transitions in models with extended scalar sectors

The effective potential is a widely used phenomenological tool to investigate phase transitions occurring in the early Universe at finite temperature. In the standard perturbative treatment the potential becomes complex in some region of the background field values due to the non-convex nature of the classical potential in models with spontaneous symmetry breaking. The imaginary part renders the minimization of the potential impossible when at finite temperature the absolute minimum is in the complex region. In this talk we introduce a simple method to calculate an effective potential that is fully real based on the optimized perturbation theory scheme. We apply the method for models that extend the Standard Model with an additional singlet scalar.