Scalar-Tensor theories from $\Lambda(\phi)$ Plebanski gravity

TL;DR

This paper reformulates scalar-tensor theories as constrained BF theories derived from a modified Plebanski action, clarifying conditions for reality and stability, and exploring matter coupling and dark matter phenomenology.

Contribution

It identifies a subclass of modified Plebanski actions equivalent to scalar-tensor theories, clarifies reality conditions, and discusses matter coupling and dark matter implications.

Findings

Scalar-tensor theories can be derived from a modified Plebanski action.

Real bivectors lead to stable scalar-tensor theories with Lorentzian metrics.

Matter coupling naturally includes scalar field dark matter phenomenology.

Abstract

We study a modification of the Plebanski action, which generically corresponds to a bi-metric theory of gravity, and identify a subclass which is equivalent to the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories. In this manner, scalar-tensor theories are displayed as constrained BF theories. We find that in this subclass, there is no need to impose reality of the Urbantke metrics, as also the theory with real bivectors is a scalar-tensor theory with a real Lorentzian metric. Furthermore, while under the former reality conditions instabilities can arise from a wrong sign of the scalar mode kinetic term, we show that such problems do not appear if the bivectors are required to be real. Finally, we discuss how matter can be coupled to these theories. The phenomenology of scalar field dark matter arises naturally within this framework.