Action principle for the connection dynamics of scalar-tensor theories

TL;DR

This paper introduces a first-order action for scalar-tensor gravity theories, deriving a connection dynamical formalism that links Jordan and Einstein frames, foundational for loop quantum scalar-tensor theories.

Contribution

It presents a novel first-order action leading to a connection formalism for scalar-tensor theories, bridging Jordan and Einstein frames, and underpinning loop quantum gravity approaches.

Findings

Derived connection formalism from the action

Established equivalence between Jordan and Einstein frames

Recovered the action principle for loop quantum scalar-tensor theories

Abstract

A first-order action for scalar-tensor theories of gravity is proposed. The Hamiltonian analysis of the action gives the desired connection dynamical formalism, which was derived from the geometrical dynamics by canonical transformations. It is shown that this connection formalism in Jordan frame is equivalent to the alternative connection formalism in Einstein frame. Therefore, the action principle underlying loop quantum scalar-tensor theories is recovered.