Systematic bias from waveform modeling for binary black hole populations in next-generation gravitational wave detectors

Next-generation gravitational wave detectors such as the Einstein Telescope and Cosmic Explorer will have increased sensitivity and observing volumes, enabling unprecedented precision in parameter estimation. However, this enhanced precision could also reveal systematic biases arising from waveform modeling, which may impact astrophysical inference. We investigate the extent of these biases over a year-long observing run with $10^5$ simulated binary black hole sources using the linear signal approximation. To establish a conservative estimate, we sample binaries from a smoothed truncated power-law population model and compute systematic parameter biases between the IMRPhenomXAS and IMRPhenomD waveform models. For sources with signal-to-noise ratios above 100, we estimate statistically significant parameter biases in $\sim 3\%-20\%$ of the events, depending on the parameter. We find that the average mismatch between waveform models required to achieve a bias of $\leq 1\sigma$ for $99\%$ of detections with signal-to-noise ratios $\geq 100$ should be $\mathcal{O}(10^{-5})$, or at least one order of magnitude better than current levels of waveform accuracy.