  In this paper, we investigate the dynamics of the confinement-deconfinement
phase transition in a toy model where the walking dynamics is realized
perturbatively. We study the properties of the phase transition focusing on the
possible cosmological signatures it can provide. Interestingly the model is
well under perturbative control only when the mass of the lightest field - the
dilaton/scalon is much lighter than the rest of the fields and the phase
transition proceeds slowly leading to strong signals in the stochastic
gravitational wave spectrum.
