Quasar Proper Motions and Low-Frequency Gravitational Waves

We report observational upper limits on the mass-energy of the cosmological gravitational wave background, from limits on proper motions of quasars. Gravitational waves with periods longer than the time span of observations produce a simple pattern of apparent proper motions over the sky, composed primarily of second-order transverse vector spherical harmonics. A fit of such harmonics to measured motions yields a 95% confidence limit on the mass-energy of gravitational waves with frequencies ν < 2 × 10-9 Hz, of less than 0.11 h-2 times the closure density of the universe.