Modified gravity with an extra force: Lagrangian description and stability
Faraoni, Valerio (Bishop\)

We revisit the issue of the correct Lagrangian description of a perfect fluid in theories of modified gravity with an extra force, in which galactic luminous matter couples nonminimally to the Ricci scalar and explains away dark matter. Two alternative Lagrangians (giving dark matter phenomenology or zero effects, respectively) are shown to be inequivalent when the fluid couples minimally to gravity; in the presence of nonminimal coupling they give rise to two distinct theories with completely different predictions. A necessary and sufficient criterion to avoid the notorious Dolgov-Kawasaki instability is also presented. (Based on V. Faraoni, Phys. Rev. D 80, 124040; Phys. Rev. D 76, 127501.)