Induced gravity and cosmological principle

The phenomenological description of the cosmological particle production in the framework of the induced gravity is investigated. It appears that the source terms with the particle number density in the creation law can be interpreted as the invisible part of the Universe. It is shown that there is a gauge that restores the General Relativity in which our model is equivalent to the $f(R)$-gravity for $f \propto R^{\frac{3}{2}}$