  We study the evolution and power spectrum of primordial gravitational waves
in the interactive Bose-Einstein gas model for dark energy, relevant, as it
addresses the coincidence problem. The model is applied in the radiation,
matter and dark-energy domination stages. The model introduces a scale factor
associated to the radiation-matter transition which influences the
gravitational spectrum. We focus on the impact of the free parameters on both
the gravitational waves amplitude and its power-spectrum slope. For sets of
parameters fitting Hubble's law, we show that the model's parameter for today's
dark-matter energy density has a noticeable impact on such waves, while the
others produce an indistinguishable effect. The feasibility of detecting such
waves under present and future measurements is discussed.
