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The gravitational wave background (GWB, or GW background or in context, stochastic background) is the ongoing low-level random gravitational wave signal that is the combination of signals from sources too weak and/or distant to stand out from the rest. It creates difficulty in isolating the GW signal of any specific source. However, it is of interest in its own right for revealing levels of activity throughout the universe, and identification of its signal it would further-confirm the general theory, and its measurement is key to the process of separating it from individual signals that might be detected.
Regarding interest in the signal itself, observation of the background may say something about the frequency of the events that have been detected, e.g., black hole mergers and neutron star mergers, and may also say something about the mass distribution across the universe and its history, which are of cosmological interest. Like the CMB, any anisotropy is of much interest.