Gravitational Waves and the Reparameterization-Invariant Hamiltonian Formalism

A consistent perturbation theory is formulated on the basis of a recently proposed method of reparameterization-invariant Hamiltonian reduction, and a linearized limit in the oscillator approximation of General Relativity is considered. Possible physical consequences of interpreting the nonzero local Hamiltonian as the gravitational field energy are discussed. The physical and geometrical meanings of reduced action variables are investigated. A qualitative conclusion is drawn about the dependence of the distribution of phases of relict gravitational waves at the current epoch on the initial conditions at the time of the Big Bang.[PUBLICATION ABSTRACT]