Abstract
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.
Highlights
General relativity forms our understanding of spacetime
There are reasons to believe that general relativity is unable to provide an adequate description of gravitational phenomena in the high energy regime and should be either modified or replaced by a new theory of gravity [7,8,9,10,11]
Inflation takes place at the early stage of a universe’s expansion, in the high energy regime, and should be driven either by a new scalar field [15] or by quantum effects associated with high order gravitational terms [16]
Summary
General relativity forms our understanding of spacetime. It is verified by the Solar System and cosmological tests [1,2]. CCGR is founded in a series of techniques, which may resolve some of general relativity’s issues appearing in the quantum regime. These are techniques for nonlinear symmetry representation (used to implement the Ogievetsky theorem [23,24,25,26]), the Hamiltonian formalism [27,28], conformal coupling of matter to gravity [29,30,31]. Parameterization-invariant time [32,33,34,35] This approach was presented in a broad series of papers [36,37,38], and our main aim is to present it in a self-consistent comprehensive form.
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