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.