  We examine a cosmological scenario where dark matter is coupled to a variable
vacuum energy while baryons and photons are two decoupled components for a
spatially flat Friedmann-Robertson-Walker spacetime. We apply the $\chi^{2}$
method to the updated observational Hubble data for constraining the
cosmological parameters and analyze the amount of dark energy in the radiation
era. We show that our model fulfills the severe bound of $\Omega_{x}(z\simeq
1100)<0.009$ at the $2\sigma$ level, so it is consistent with the recent
analysis that includes cosmic microwave background anisotropy measurements from
the Planck survey, the Atacama Cosmology Telescope, and the South Pole
Telescope along with the future constraints achievable by the Euclid and CMBPol
experiments, and fulfills the stringent bound $\Omega_{x}(z\simeq
10^{10})<0.04$ at the $2\sigma$ level in the big-bang nucleosynthesis epoch.
