  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.
