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We report observational upper limits on the mass-energy of the cosmologicalgravitational-wave background, from limits on proper motions of quasars.Gravitational waves with periods longer than the time span of observationsproduce a simple pattern of apparent proper motions over the sky, composedprimarily of second-order transverse vector spherical harmonics. A fit of suchharmonics to measured motions yields a 95%-confidence limit on the mass-energyof gravitational waves with frequencies <2e-9 Hz, of <0.11/h*h times theclosure density of the universe.

Quasar Proper Motions and Low‐Frequency Gravitational Waves