Probability distribution function of the coarse-grained scalar field at finite temperature Original Research Article

We present a formalism to calculate the probability distribution function of a scalar field coarsegrained over some spatial scales with a Gaussian filter at finite temperature. As an application, we investigate the role of subcritical fluctuations in the electroweak phase transition in the minimal standard model. It is concluded that the universe was in a mixed state of true and false vacua already at the critical temperature.