Uncertainty in predicting the stochastic gravitational wave background from compact binary coalescences

The stochastic gravitational wave background from compact binary coalescences is expected to be the first detectable stochastic signal via cross-correlation searches with terrestrial detectors. It encodes the cumulative merger history of stellar-mass binaries across cosmic time, offering a unique probe of the high-redshift Universe. However, predicting the background spectrum is challenging due to numerous modeling choices, each with distinct uncertainties. In this work, we present a comprehensive forecast of the astrophysical gravitational wave background from binary black holes, binary neutron stars, and neutron star-black hole systems. We systematically assess the impact of uncertainties in population properties, waveform features, and the modeling of the merger rate evolution. By combining all uncertainties, we derive credible bands for the background spectrum, spanning approximately an order of magnitude in the fractional energy density. These results provide thorough predictions to facilitate the interpretation of current upper limits and future detections.