  Extending the renormalizability proposal of the physical sector of 4D
Einstein gravity, we have recently proposed renormalizability of the 3D
physical sector of gravity-matter systems. The main goal of the present work is
to conduct systematic one-loop renormalization of a gravity-matter system by
applying our foliation-based quantization scheme. In this work we explicitly
carry out renormalization of a gravity-scalar system with a Higgs-type
potential. With the fluctuation part of the scalar field gauged away, the
system becomes renormalizable through a metric field redefinition. We use
dimensional regularization throughout. One of the salient aspects of our
analysis is how the graviton propagator acquires the"mass" term. One-loop
calculations lead to renormalization of the cosmological and Newton's
constants. We discuss other implications of our results as well: time-varying
vacuum energy density and masses of the elementary particles as well as the
potential relevance of Neumann boundary condition for black hole information.
