  Recently, an interesting gravitational model was proposed in order to mimic
the effect of Dark Matter. Chamseddine and Mukhanov in the arXiv preprint
1308.5410 have separated the conformal mode of a physical metric in the form of
a squared gradient of an auxiliary scalar field. Notably, the variational
principle has given a more general equation of motion than that of purely
Einsteinian relativity theory, with a possibility of reproducing an effective
Dark Matter. In this short paper, we explain the nature of this phenomenon in
terms of the class of functions on which the variation takes place. Then we
give a more transparent equivalent formulation of the model without an
auxiliary metric. Finally, we speculate a bit about possible extensions.
