Application of the Background Field Method to Cosmological Phase Transitions at Finite Temperature and Chemical Potential - Nhu Xuan, Nguyen; Toan Thang, Vu (VNU Journal of Science: Mathematics - Physics, 2026)
We investigate cosmological phase transitions using the background field method (BFM) within finite-temperature quantum field theory. The one-loop thermal free energy density is calculated at high temperature and nonzero chemical potential in order to analyze spontaneous symmetry breaking in the early Universe. By constructing the effective potential in momentum space, we obtain analytical expressions and perform numerical evaluations. The results demonstrate that a first-order phase transition may occur at sufficiently high temperature and chemical potential, characterized by discontinuities in the effective scalar mass and the free energy density. Furthermore, symmetry non-restoration at high temperature is observed, suggesting a persistent asymmetry in the post-transition Universe. These findings highlight the relevance of gauge-invariant and non-perturbative methods for the study of cosmological phase transitions.