Degenerate Limits of Scalar-Tensor Gravity

We study the degenerate limits of the scalar-tensor theory of gravity in its Hamiltonian connection dynamics formulation. The degenerate limit of the spatial triad is effectuated by a local scaling transformation of the triad, which leads to the degenerate limits of all other geometric quantities and relations in the connection dynamics. We derive the constraints for the degenerate scalar-tensor theory of gravity and discuss their physical implications.