  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.
