Graviton Mass Bounds

TL;DR

The paper surveys whether gravitons can be massive and how to bound such mass across theory and observation. It contrasts Lorentz-invariant and violating massive gravity, outlining three model-independent bound classes—Yukawa potential, modified dispersion relation, and fifth force—and highlights the direct GW150914 constraint m_g < 1.2×10^-22 eV while comparing with solar-system, lensing, and cosmological bounds. Central to the discussion is the Vainshtein mechanism and Galileon structure, which reconcile linear bounds with GR in many regimes, and the review catalogs current and projected bounds, including multi-messenger and CMB-based probes. The authors emphasize that upcoming detectors like eLISA and future pulsar timing arrays will further tighten the graviton-mass bounds, potentially to the 10^-24–10^-32 eV range depending on environment and model class.

Abstract

Recently, aLIGO has announced the first direct detections of gravitational waves, a direct manifestation of the propagating degrees of freedom of gravity. The detected signals GW150914 and GW151226 have been used to examine the basic properties of these gravitational degrees of freedom, particularly setting an upper bound on their mass. It is timely to review what the mass of these gravitational degrees of freedom means from the theoretical point of view, particularly taking into account the recent developments in constructing consistent massive gravity theories. Apart from the GW150914 mass bound, a few other observational bounds have been established from the effects of the Yukawa potential, modified dispersion relation and fifth force that are all induced when the fundamental gravitational degrees of freedom are massive. We review these different mass bounds and examine how they stand in the wake of recent theoretical developments and how they compare to the bound from GW150914.

Figures (3)

• Figure 1: The six modes for a massive spin--2 field. The two tensor modes and the scalar conformal mode are propagating out of the page; the two vector modes and the longitudinal scalar mode are propagating to the right (taken from deRham:2014zqa).
• Figure 2: A schematic sketch of B--mode power spectra for a range of graviton masses (See Fig. 3 of Dubovsky:2009xk for more details). We use $H_r$ as the Hubble parameter at recombination. A characteristic plateau appears at $\ell<100$ when the graviton mass is of the order of the Hubble parameter at recombination. When $m_g$ is much bigger or smaller than $H_r$, the low $\ell$ power spectrum is, on the other hand, suppressed.
• Figure 3: Allowed tree level graviton decay diagram if the graviton is massive (and one can go in its rest frame).