Nonlinear Properties of Vielbein Massive Gravity

TL;DR

This paper introduces a nonlinear extension of massive gravity using a vielbein formulation, demonstrating improved ultraviolet behavior and a specific decoupling limit.

Contribution

It presents a novel nonlinear vielbein-based massive gravity model derived from bi-gravity, with a detailed analysis of its decoupling limit and ultraviolet properties.

Findings

Model exhibits the softest UV behavior, becoming strong only at Lambda_3 scale.

Decoupling of tensor, vector, and scalar Stueckelberg fields in a specific gauge.

Reduces to a cosmological constant in a particular limit.

Abstract

We propose a non-linear extension of the Fierz-Pauli mass for the graviton through a functional of the vielbein and an external Minkowski background. The functional generalizes the notion of the measure, since it reduces to a cosmological constant if the external background is formally sent to zero. Such a term and the explicit external background, emerge dynamically from a bi--gravity theory, having both a massless and a massive graviton in its spectrum, in a specific limit in which the massless mode decouples, while the massive one couples universally to matter. We investigate the massive theory using the Stueckelberg method and providing a 't Hooft-Feynman gauge fixing in which the tensor, vector and scalar Stueckelberg fields decouple. We show that this model has the softest possible ultraviolet behavior which can be expected from any generic (Lorentz invariant) theory of massive gravity, namely that it becomes strong only at the scale Lambda_3 = (m_g^2 M_P)^{1/3}.