Phases of massive gravity

TL;DR

The paper systematically analyzes the most general Lorentz-violating graviton mass term preserving 3D Euclidean symmetry, using a covariant Stückelberg framework to study the Goldstone sector. It shows that generic mass choices yield six propagating modes with ghosts or instabilities, but identifies several finely-tuned and symmetry-protected regions where a consistent low-energy EFT with cutoff Λ ~ √(m M_Pl) exists, including two UV-insensitive theories with reduced diffeomorphism symmetry. It demonstrates the absence of the vDVZ discontinuity in the viable regions and explores rich cosmological implications, such as the possibility of large graviton masses affecting structure formation and backreaction. The work highlights both the potential viability of Lorentz-violating massive gravity models and the significant open questions about stability, UV completion, and observational constraints.

Abstract

We systematically study the most general Lorentz-violating graviton mass invariant under three-dimensional Eucledian group using the explicitly covariant language. We find that at general values of mass parameters the massive graviton has six propagating degrees of freedom, and some of them are ghosts or lead to rapid classical instabilities. However, there is a number of different regions in the mass parameter space where massive gravity can be described by a consistent low-energy effective theory with cutoff $\sim\sqrt{mM_{Pl}}$ free of rapid instabilities and vDVZ discontinuity. Each of these regions is characterized by certain fine-tuning relations between mass parameters, generalizing the Fierz--Pauli condition. In some cases the required fine-tunings are consequences of the existence of the subgroups of the diffeomorphism group that are left unbroken by the graviton mass. We found two new cases, when the resulting theories have a property of UV insensitivity, i.e. remain well behaved after inclusion of arbitrary higher dimension operators without assuming any fine-tunings among the coefficients of these operators, besides those enforced by the symmetries. These theories can be thought of as generalizations of the ghost condensate model with a smaller residual symmetry group. We briefly discuss what kind of cosmology can one expect in massive gravity and argue that the allowed values of the graviton mass may be quite large, affecting growth of primordial perturbations, structure formation and, perhaps, enhancing the backreaction of inhomogeneities on the expansion rate of the Universe.

Figures (1)

• Figure 1: Splitting of zeroes of the eigenvalue of the matrix $M$ due to higher-derivative terms in the presence of residual symmetry (\ref{['xx']}) in two different cases: a) $m_1^2\;,\;m_0^2>0$, b) $m_1^2\;,\;m_0^2<0$