Understanding the impact of compact binary population uncertainties for the detection of the gravitational-wave background

The LIGO-Virgo-KAGRA collaboration has observed tens of binary black holes so far, which have been used in several studies to infer the features of the underlying binary black hole population. From these, it is possible to predict the overall gravitational-wave (GW) fractional energy density (Ω_GW) due to black holes throughout the Universe, and thus estimate the gravitational-wave background (GWB) spectrum we may measure in GW detectors. These predictions are fundamental in our forecasts for background detection and characterization, with both present and future instruments. The uncertainties in the inferred population strongly impact the predicted energy spectrum, and in this talk we present a new, flexible method to quickly calculate the energy spectrum for varying black hole population features such as the mass spectrum and redshift distribution. We discuss how uncertainties in these distributions impact our detection capabilities and present several caveats for background estimation.