Dark matter interacts with variable vacuum energy

We investigate a spatially flat Friedmann-Robertson-Walker scenario with two interacting components, dark matter and variable vacuum energy densities, plus two decoupled components, one is a baryon term while the other behaves as a radiation component. We consider a linear interaction in the derivative dark component density. We apply the chi(2) method to the observational Hubble data for constraining the cosmological parameters and analyze the amount of dark energy in the radiation era for the model. It turns out that our model fulfills the severe bound of Omega(x) (z similar or equal to 1,100) < 0.009 at 2 sigma level, so is consistent with the recent analysis that include cosmic microwave background anisotropy measurements from Planck survey, the future constraints achievable by Euclid and CMBPol experiments, reported for the behavior of the dark energy at early times, and fulfills the stringent bound Omega(x) (z similar or equal to 10(10)) < 0.04 at 2 sigma level in the big-bang nucleosynthesis epoch. We also examine the cosmic age problem at high redshift associated with the old quasar APM 08279+5255 and estimate the age of the universe today.