The Brans–Dicke–Rastall theory

We formulate a theory combining the principles of scalar–tensor gravity and Rastall’s proposal of a violation of the usual conservation laws. We obtain a scalar–tensor theory with two parameters (Formula presented.) and (Formula presented.), the latter quantifying the violation of the usual conservation laws ((Formula presented.) corresponding to the General Relativity limit). The only exact spherically symmetric solution is that of Robinson–Bertotti besides the Schwarzschild solution. A PPN analysis reveals that General Relativity results are reproduced when (Formula presented.). The cosmological case displays a possibility of deceleration/acceleration or acceleration/deceleration transitions during the matter dominated phase depending on the values of the free parameters.