Baryonic matter perturbations in decaying vacuum cosmology

We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a $\Lambda(t)$CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillation (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influenced by the baryons, there are modifications on the perturbative level if a separately conserved baryon fluid is included. Considering the present baryon fraction as a free parameter, we reproduce the observed abundance of the order of $5\%$ independently of the dark-matter abundance which is of the order of $32\%$ for this model. Generally, the concordance between background and perturbation dynamics is improved if baryons are explicitly taken into account.