Gravitational waveform accuracy requirements for current and future ground-based detectors

Next-generation (XG) Gravitational-Wave (GW) detectors of the coming decade, such as Cosmic Explorer and Einstein Telescope, will enable detailed studies of stellar mass binary black hole (BBH) mergers across the Universe. Accurate waveform models are crucial for inferring binary parameters, including black hole (BH) masses and spins from a GW signal. These models are created from numerical relativity (NR) simulations and semi-analytical expressions during the inspiral phase. We evaluate the limitations of current waveform models using multiple likelihood models to determine the signal-to-noise ratio above which systematic biases will dominate our inferences for prominent BBH systems, leading to potential wrongful scientific conclusions at higher sensitivities. For XG detectors, we will require semi-analytical waveform models to be at least two orders of magnitude more accurate and improvements of one order of magnitude for NR waveforms. Biases in the inferred mass, luminosity distance, inclination of the binary orbit, and spin parameters are significant for XG networks, which may impact future BH populations and cosmological studies. Addressing these challenges requires the development of more comprehensive and accurate waveform models, alongside crucial advancements in the efficiency of NR codes in the coming decade, to fully capitalize on the scientific potential of XG detector networks.