Vacuum degeneracy in Massive gravity=Multiplicity of fundamental scales

TL;DR

This paper explores how Nambu-Goldstone bosons cause vacuum degeneracy in massive gravity, leading to multiple fundamental scales interconnected by broken symmetries, affecting gravitational observations.

Contribution

It reveals the link between vacuum degeneracy and the multiplicity of fundamental scales in massive gravity due to Nambu-Goldstone bosons.

Findings

Vacuum solutions exhibit degeneracy similar to sigma-models.

Different fundamental scales are connected via broken symmetry generators.

Gravitational effects influence the perceived degeneracy at various distances.

Abstract

The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions of the non-linear formulations of massive gravity in the same spirit of the $\sigma$-models. When the gravitational effects are taken into account, and the observers are located at any distance with respect to the source, this degeneracy corresponds to a multiplicity (flow) of the fundamental scales of the theory. The different values of the fundamental scales are connected each other through the broken generators of the theory.