  The composite Higgs model assumes that the Higgs field arises as the
pseudo-Goldstone mode corresponding to a dynamical symmetry breaking in a new
strongly coupled sector. We present a soft-wall holographic model where such
symmetry breaking occurs as a first order phase transition. In this case the
bubble nucleation in the early universe becomes possible. To study the
homogeneous solutions in the models of this type we present the perturbation
theory approach. We estimate the gravitational wave spectrum produced during
the nucleation phase and find it to be detectable with the planned
gravitational wave detectors.
