Degenerate Limits of Scalar-Tensor Gravity

Abstract

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.

9 pages

References in corpus (23)

• f(R) Theories Of Gravity
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Real and complex connections for canonical gravity
• Loop quantum cosmology of Bianchi I models
• Carroll versus Galilei Gravity
• Extension of loop quantum gravity to $f(R)$ theories
• Loop quantum $f(R)$ theories
• Nonperturbative Loop Quantization of Scalar-Tensor Theories of Gravity
• The loop quantum cosmology bounce as a Kasner transition
• Degenerate Extensions of General Relativity
• Loop Quantum Brans-Dicke Theory
• A trick for passing degenerate points in Ashtekar formulation
• Generalized Ashtekar variables for Palatini f(R) models
• Hamiltonian form of `Carroll' gravity
• Matter in Loop Quantum Gravity without time gauge: a non-minimally coupled scalar field
• Connection Dynamics for Higher Dimensional Scalar-Tensor Theories of Gravity
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Equivalence of scalar-tensor theories and scale-dependent gravity
• Loop Quantum Vector-Tensor Gravity and Its Spherically Symmetric Model
• Quantum geometric formulation of Brans-Dicke theory for Bianchi I spacetime
• Canonical Gravity in Degenerate Limit
• Deparametrization and quantization of scalar-tensor gravity and its cosmological model