Gravitational waves in Intrinsic Time Geometrodynamics

Gravitational waves are investigated in Intrinsic Time Geometrodynamics. This theory has a non-vanishing physical Hamiltonian generating intrinsic time development in our expanding universe, and four-covariance is explicitly broken by higher spatial curvature terms. Linearization of Hamilton's equations about the de Sitter solution produces transverse traceless excitations, with the physics of gravitational waves in Einstein's General Relativity recovered in the low curvature low frequency limit. A noteworthy feature of the theory is that gravitational waves always carry positive energy density, even for compact spatial slicings without any energy contribution from boundary Hamiltonian. This study of gravitational waves in compact $k= +1$ cosmological de Sitter spacetime is in contradistinction to, and complements, previous $k= -1$ investigations of Hawking, Hertog and Turok and other more familiar $k=0$ works. In addition, possible non-four-covariant Horava gravity contributions are considered (hence the use of canonical Hamiltonian, rather than Lagrangian, methods). Recent explicit $S^3$ transverse-traceless mode spectrum of Lindblom, Taylor and Zhang are also employed to complete the discussion.