Is the continuous matter creation cosmology an alternative to
  $\Lambda$CDM?
  The matter creation cosmology is revisited, including the evolution of
baryons and dark matter particles. The creation process affects only dark
matter and not baryons. The dynamics of the $\Lambda$CDM model can be
reproduced only if two conditions are satisfied: 1) the entropy density
production rate and the particle density variation rate are equal and 2) the
(negative) pressure associated to the creation process is constant. However,
the matter creation model predicts a present dark matter-to-baryon ratio much
larger than that observed in massive X-ray clusters of galaxies, representing a
potential difficulty for the model. In the linear regime, a fully relativistic
treatment indicates that baryons are not affected by the creation process but
this is not the case for dark matter. Both components evolve together at early
phases but lately the dark matter density contrast decreases since the
background tends to a constant value. This behaviour produces a negative growth
factor, in disagreement with observations, being a further problem for this
cosmology.
