# Note on massless and partially massless spin-2 particles in a curved background via a nonsymmetric tensor

## TL;DR

This paper explores the propagation of massless and partially massless spin-2 particles in curved backgrounds using a nonsymmetric tensor framework, extending previous models and identifying conditions for consistent propagation.

## Contribution

It introduces a new analysis of massless and partially massless spin-2 theories in curved spaces using nonsymmetric tensors, revealing specific parameter conditions for consistent propagation.

## Key findings

- Massless spin-2 particles propagate in maximally symmetric spaces for a specific parameter value.
- A non-symmetric scalar-tensor model emerges for other parameter values.
- Partially massless models are also examined within this framework.

## Abstract

In the last few years we have seen an increase interest on gravitational waves due to recent and striking experimental results confirming Einstein's general relativity once more. From the field theory point of view, gravity describes the propagation of self-interacting massless spin-2 particles. They can be identified with metric perturbations about a given background metric. Since the metric is a symmetric tensor, the massless spin-2 particles present in the Einstein-Hilbert (massless Fierz-Pauli) theory are naturally described by a symmetric rank-2 tensor. However, this is not the only possible consistent massless spin-2 theory at linearized level. In particular, if we add a mass term, a new one parameter $(a_1)$ family of models ${\cal L}(a_1)$ shows up. They consistently describe massive spin-2 particles about Einstein spaces in terms of a non-symmetric rank-2 tensor. Here we investigate the massless version of ${\cal L}(a_1)$ in a curved background. In the case $a_1=-1/12$ we show that the massless spin-2 particles consistently propagate, at linearized level, in maximally symmetric spaces. A similar result is obtained otherwise $(a_1 \ne -1/12)$ where we have a non-symmetric scalar-tensor massless model. The case of partially massless non-symmetric models is also investigated.