Reparametrization-invariant Hamiltonian formalism in general relativity

A method of Hamiltonian constraint resolution which leads to invariant under the parametrization reduced theory with a well-defined local nonzero Hamiltonian function was proposed. This method is based on introducing the global (depending just on time) conformal variable. The geometrical and physical meaning of variables in reduced action is investigated. It is shown that there are no contradictions with perturbation theory. The absence of wave-like excitations of gravity with negative contribution to the reduced Hamiltonian is shown. The analysis of linear approximation of the reduced classical theory shows that in Early Universe the effective state equation for gravity matter is the maximal rigid state equation