The Layzer-Irvine equation in theories with non-minimal coupling between   matter and curvature
  We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles. 
Orfeu Bertolami and Claudio Gomes
astro-ph.CO gr-qc