Cosmology from a Lagrangian formulation for Rastall's theory

We give a Lagrangian formulation for the theory of Rastall of gravitation. After proposing a Lagrangian density that reproduces the equations of motion postulated by Rastall, we study the cosmological consequences and fit the parameters using recent data from Hubble function $H(z).$ According to two model selection criteria, one based on corrected Akaike Information Criterion (AICc) and another on Bayesian Information Criterion (BIC), known to penalize models with a greater number of parameters, particularly BIC, we obtain some competitive models relative do $\Lambda CDM.$ In one of these models the cosmological constant is interpreted as having origin in the creation of matter due to time dependent gravitational field, as opposed to the origin in the vacuum energy.