How to Constrain the Stochastic Gravitational Wave Background with Multi-Frequency Detections

Gravitational wave (GW) observations probe both a diffuse, stochastic gravitational wave background (SGWB) as well as individual cataclysmic events such as the merger of two compact objects. The detection and description of the gravitational-wave background requires somewhat different techniques than required for individual events. In this paper, we probe the sensitivity of present and future GW telescopes to different background sources, including both those expected from unresolved compact binaries in both their quasi-Newtonian quiescent and their eventual mergers, as well as more speculative cosmological sources such as inflation, cosmic strings, and phase transitions, over regions in which those sources can be described by a single power aw. We develop a Fisher matrix formalism to forecast coming sensitivities of single and multiple experiments, and novel visualizations taking into account the increase in sensitivity to a background over time.