Abstract
We consider an extended theory of gravity with Lagrangian [Formula: see text], with [Formula: see text] being a [Formula: see text]th-order invariant made of contractions of the energy–momentum tensor. When [Formula: see text], this theory reduces to [Formula: see text] gravity, where [Formula: see text] accounts for the trace of the energy–momentum tensor. We study the gravitational wave polarization modes, from which it results that when the matter Lagrangian contains dynamical scalar fields minimally coupled to the geometry, further polarization modes arise with respect to General Relativity. Finally, we show that the motion for test particles is nongeodesic and we explicitly obtain the extra force.
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