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aggregation of matter anomaly Astron Astrophys bi-scalar big-bang universe canonical canonical quantization collapse constant constraint equations corresponds cosmic expansion cosmic turbulence cosmological background cosmological constant denotes density contrast density perturbations derived dissipation dynamical easily seen eddies Einstein's field equations energy epoch equations of motion expanding universe expression follows from Eqs formalism Friedmann function galaxies gauge given by Eq gravitational collapse gravitational field gravitational instability gravitons Green's function Hamiltonian Hiroshima University homogeneous inserting Eq integration isotropic Kimura Lagrangian density mass metric metric tensor model-universe Moreover Nariai Newtonian hydrodynamics non-linear obtain Ozernoi pair-creation parameter Phys positive frequency problem Prog propagation quantities quantized scalar field quantum radiation reduced relation relativistic relativity respectively right-hand side satisfies Sato scalar field Sitter universe solution space-time spatial spherical symmetry stage Supergalaxy tensor term Theoretical Physics theory of gravitation tion Tomita transformation variables velocity