Searching for a Stochastic Background of Gravitational Waves with the Laser Interferometer Gravitational-Wave Observatory

The Laser Interferometer Gravitational-Wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new Bayesian 90% upper limit is Omega(GW) x [H(0)/72 km s(-1) Mpc(-1))](2) < 6.5 x 10(-5). This is currently the most sensitive result in the frequency range 51-150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss the complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.