Constraints on Massive-Graviton Dark Matter from Pulsar Timing and Precision Astrometry

The effect of a narrow-band isotropic stochastic gravitational wave background on pulsar timing and astrometric measurements is studied. Such a background appears in some theories of gravity. We show that the existing millisecond pulsar timing accuracy ($\sim 0.2\mu \mathrm{s}$) strongly constrains possible observational consequences of theory of massive gravity with spontaneous Lorentz braking, essentially ruling out significant contribution of massive gravitons to the local dark halo density. The present-day accuracy of astrometrical measurements ($\sim 100\mu \mathrm{arc}\sec$) sets less stringent constraints on this theory.

Figure 1

Astrometric (dot-dashed lines) and pulsar timing (solid line) constraints on the overall energy density of a stationary isotropic background of monochromatic GWs as a function of the frequency $\nu$ in the range $\sim {10}^{-8}<\nu <\sim 3\times {10}^{-5}\mathrm{Hz}$ allowed by binary pulsar GW emission and dark matter (DM) clustering constraints (see Introduction). The thick dashed line corresponds to the local DM energy density of $0.3\mathrm{GeV}{\mathrm{cm}}^{-3}$. The constraint in the lower right-hand corner of the graph is set by the Doppler tracking of the Cassini spacecraft [16].