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Infrared-modified gravities and massive gravitons

V. A. Rubakov, P. G. Tinyakov

TL;DR

The paper surveys infrared-modified gravities, contrasting the problematic Lorentz-invariant Fierz–Pauli theory with healthier Lorentz-violating alternatives. It uses the Stückelberg–Goldstone formalism to analyze propagating modes, ghosts, and strong coupling, and discusses how residual symmetries or ghost-condensate mechanisms can yield viable IR modifications. Key results include the absence of the vDVZ discontinuity and BD instabilities in certain Lorentz-violating models, the existence of a ghost-condensate sector with a slow $\omega^2\propto p^4$ mode, and a minimal Healthy model with distinctive cosmological and black-hole phenomenology. The work emphasizes potential observational signatures in structure formation, gravitational waves, and black-hole physics, while noting unresolved questions about UV completion and full non-linear dynamics.

Abstract

We review some theoretical and phenomenological aspects of massive gravities in 4 dimensions. We start from the Fierz--Pauli theory with Lorentz-invariant mass terms and then proceed to Lorentz-violating masses. Unlike the former theory, some models with Lorentz-violation have no pathologies in the spectrum in flat and nearly flat backgrounds and lead to interesting phenomenology.

Infrared-modified gravities and massive gravitons

TL;DR

The paper surveys infrared-modified gravities, contrasting the problematic Lorentz-invariant Fierz–Pauli theory with healthier Lorentz-violating alternatives. It uses the Stückelberg–Goldstone formalism to analyze propagating modes, ghosts, and strong coupling, and discusses how residual symmetries or ghost-condensate mechanisms can yield viable IR modifications. Key results include the absence of the vDVZ discontinuity and BD instabilities in certain Lorentz-violating models, the existence of a ghost-condensate sector with a slow mode, and a minimal Healthy model with distinctive cosmological and black-hole phenomenology. The work emphasizes potential observational signatures in structure formation, gravitational waves, and black-hole physics, while noting unresolved questions about UV completion and full non-linear dynamics.

Abstract

We review some theoretical and phenomenological aspects of massive gravities in 4 dimensions. We start from the Fierz--Pauli theory with Lorentz-invariant mass terms and then proceed to Lorentz-violating masses. Unlike the former theory, some models with Lorentz-violation have no pathologies in the spectrum in flat and nearly flat backgrounds and lead to interesting phenomenology.

Paper Structure

This paper contains 31 sections, 271 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Fierz-Pauli model
  3. Lorentz-invariant massive gravity in Minkowski background
  4. Ghost via Stückelberg trick
  5. Van Dam--Veltman--Zakharov discontinuity
  6. Vainshtein radius
  7. Strong coupling
  8. Fierz--Pauli theory in curved backgrounds: Boulware--Deser mode
  9. Cosmological background
  10. Stückelberg treatment
  11. Lorentz-violating theories: generalities
  12. Lorentz-violating mass terms
  13. Eliminating the second scalar mode
  14. $m_0 = 0$
  15. $m_1 = 0$
  16. ...and 16 more sections

Figures (2)

  • Figure 1: Four-graviton scattering in the first two orders of the perturbation theory (panels $a$ and $b$, respectively). Only $s$-channel diagram is shown in the second order, panel $b$.
  • Figure 2: The decay of the vacuum into two ghosts and two photons via creation of a virtual graviton pair.