Conformally Coupled General Relativity

The gravity model developed in the series of papers (Arbuzov et al. 2009; 2010), (Pervushin et al. 2012) is revisited. The model is based on the Ogievetsky theorem, which specifies the structure of the general coordinate transformation group. The theorem is implemented in the context of the Noether theorem with the use of the nonlinear representation technique. The canonical quantization is performed with the use of reparametrization-invariant time and Arnowitt– Deser–Misner foliation techniques. Basic quantum features of the models are discussed. Mistakes appearing in the previous papers are corrected.