The Brans-Dicke-like field of scalar-tensor gravity can be described as an imperfect fluid in an approach in which the field equations are regarded as effective Einstein equations. After completing this approach, we recover, as a special case, the known effective fluid for a scalar coupled nonminimally to the Ricci curvature, and we describe the imperfect fluid equivalent of $f(R)$ gravity. A symmetry of electrovacuum Brans-Dicke gravity is translated into a symmetry of the corresponding effective fluid. The discussion is valid for any spacetime geometry.

• Received 13 August 2018

DOI:https://doi.org/10.1103/PhysRevD.98.084019