Higher orders for cosmological phase transitions: a global study in a Yukawa model

We perform a state-of-the-art global study of the cosmological thermal histories of a simple Yukawa model, and find higher perturbative orders to be important for determining both the presence and strength of strong first-order phase transitions. Using high-temperature effective field theory, we calculate the free energy density of the model up to $\mathcal{O}(y^5T^4)$, where $y$ is the Yukawa coupling and $T$ is the temperature. The locations of phase transitions are found using the results of lattice Monte-Carlo simulations, and the strength of first-order transitions are evaluated within perturbation theory, to 3-loop order. This is the first global study of any model at this order. Compared to a vanilla 1-loop analysis, accurate to $\mathcal{O}(y^2 T^4)$, reaching such accuracy enables on average a five-fold reduction in the relative error in the predicted critical temperature $T_\text{c}$, and an additional $\sim50\%$ strong first-order transitions with latent heat $L/T_\text{c}^4 > 0.1$ to be identified in our scan.