The density of states method in Yang-Mills theories and first order phase transitions

Extensions of the standard model that lead to first-order phase transitions in the early universe can produce a stochastic background of gravitational waves, which may be accessible to future detectors. Thermodynamic observables at the transition, such as the latent heat, can be determined by lattice simulations, and then used to predict the expected signatures in a given theory. In lattice calculations, the emergence of metastabilities in proximity of the phase transition may make the precise determination of these observables quite challenging, and may lead to large uncontrolled numerical errors. In this contribution, we discuss as a prototype lattice calculation the first order deconfinement transition that arises in the strong SU(3) Yang-Mills sector. We adopt the novel logarithmic linear relaxation method, which can provide a determination of the density of states of the system with exponential error suppression. Thermodynamic observables can be reconstructed with a controlled error, providing a promising direction for accurate model predictions in the future.