Consistent Thermal Resummation and Phase Transitions with 2PI Methods

Abstract

We apply the two-particle irreducible (2PI) formalism as a framework for a consistent thermal resummation in studies of cosmological phase transitions. Considering a model with two mixing real scalar fields, we work within the Hartree approximation and renormalize the 2PI effective action, while introducing a connection to physical parameters. This yields the Hartree-resummed finite-temperature effective potential, which is valid for all temperatures and avoids the limitations of conventional methods based on the high-temperature approximation. With this potential, we study one- and two-step transitions within the model, and compare our results with those obtained using resummation schemes widely employed in the literature. Finally, we evaluate the gravitational wave spectrum generated from first-order phase transitions, demonstrating the impact of the choice of resummation scheme on the predicted spectrum.