Speaker
Description
Cross-correlations between the outputs of gravitational-wave detectors can be used to detect a stochastic gravitational-wave background (SGWB). Given a pair of detectors, their outputs are correlated through a filter chosen in such a way to maximize the signal-to-noise ratio of the SGWB. I will show in two ways how to solve this optimization problem in the general case where correlations between noise in the two detectors are present. The first method reduces the problem to the Cauchy-Schwarz inequality for a suitable scalar product. The second method uses a variational strategy leading to the same result. Even after the filter optimization and the requirement that the corresponding signal-to-noise ratio of the SGWB overcomes a detection threshold, the full signal obtained by correlating the data streams of the two detectors still carries a non-vanishing contribution from pure noise correlations. Then a further requirement before claiming detection is that the contribution of the SGWB to the full signal dominates over that of noise correlations. I will illustrate some consequences of these general results, including an application to power-law backgrounds.