Pauli-Fierz mass term in modified Plebanski gravity

TL;DR

This paper explores modifications of BF theory in gravity to generate a Pauli-Fierz mass term for the graviton, analyzing the role of the Immirzi parameter and the challenges of avoiding ghost modes in bi-gravity models.

Contribution

It identifies specific potential profiles in SO(4) BF theory that produce a Pauli-Fierz mass term and examines the impact of the Immirzi parameter on graviton masses and ghost propagation.

Findings

Pauli-Fierz mass term can be realized in BF theory with specific potentials.

The Immirzi parameter influences the mass of the second graviton.

Ghost modes persist in interactions even with the Pauli-Fierz mass term.

Abstract

We study SO(4) BF theory plus a general quadratic potential, which describes a bi- metric theory of gravity. We identify the profile of the potential leading to a Pauli-Fierz mass term for the massive graviton, thereby avoiding the linearized ghost. We include the Immirzi parameter in our analysis, and find that the mass of the second graviton depends on it. At the non-perturbative level, we find a situation similar to genuine bi-gravities: even choosing the Pauli-Fierz mass term, the ghost mode propagates through the interactions. We present some simple potentials leading to two and three degrees of freedom, and discuss the difficulties of finding a ghost-free bi-gravity with seven degrees of freedom. Finally, we discuss alternative reality conditions for the case of SO(3,1) BF theory, relevant for Lorentzian signature, and give a new solution to the compatibility equation.