Brans-Dicke cosmology mimicking running vacuum

Brans-Dicke (BD) cosmology is reconsidered from an approach in which the model can be formulated in $\Lambda$CDM form, but at the expense of replacing the rigid cosmological constant $\Lambda$ with a dynamical quasivacuum component which depends on a small parameter $\epsilon$. The product of $\epsilon$ times the BD-parameter $\omega_{\rm BD}$ becomes exactly determined in terms of the ordinary cosmological parameters. The GR limit is recovered for $\omega_{\rm BD}\to\infty$ when $\epsilon\to 0$. We solve the background cosmology of the model as well as the perturbations equations. When fitted to the cosmological data, we find that the BD-cosmology, transcribed in such an effective GR form, appears to be competitive with the $\Lambda$CDM and emulates the running vacuum model.