Scalar-Tensor theory as a singular subsector of {\Lambda}({\phi}) Plebanski gravity

TL;DR

This paper demonstrates how scalar-tensor theories can be derived from Plebanski gravity by relaxing certain constraints, revealing a subclass that aligns with known scalar-tensor models.

Contribution

It introduces a novel approach to obtain scalar-tensor theories from Plebanski gravity through constraint relaxation and identifies a specific subclass matching Bergmann-Wagoner-Nordtvedt theories.

Findings

Scalar-tensor theories emerge from Plebanski gravity via constraint relaxation.

A subclass with potential depending on the trace of Lagrange multipliers is identified.

This subclass corresponds to known scalar-tensor models.

Abstract

It is shown that, in the absence of matter fields, the coupling of a scalar field to the non-chiral Plebanski action can be obtained by relaxing the trace component of the simplicity constraints. This is realized by considering a subclass of generalized theories, where a potential depending on invariants of the Lagrange multipliers is added to the Plebanski action. Generically such theories propagate eight degrees of freedom, but here the (singular) subclass with the potential only depending on the trace of the Lagrange multiplier is displayed as the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories.