Reparametrization-invariant Hamiltonian formalism in the general theory of relativity

A method is proposed that is appropriate for resolving the Hamiltonian constraint and which leads to a reparametrization-invariant reduced theory specified by a well-defined nonzero local Hamiltonian. This method is based on introducing a global (dependent only on time) conformal variable. The physical and geometric meaning of the variables in the reduced action functional is investigated. It is shown that, within the theory, the method of small perturbations is self-consistent. It is demonstrated that, in the theory of gravity, there are no wavelike excitations that make a negative contribution to the Hamiltonian. From an analysis of the reduced classical theory in the linear approximation, it follows that, at the first instants from the birth of the Universe, the extremely rigid equation of state appeared to be the effective equation of the state of gravity matter.