Gravitational waveform accuracy requirements for future ground-based detectors

Future third-generation (3G) ground-based gravitational wave (GW) detectors, such as the Einstein Telescope and Cosmic Explorer, will have unprecedented sensitivities enabling studies of the entire population of stellar mass binary black hole coalescences in the universe, while the A+ and Voyager upgrades to current detectors will significantly improve over advanced LIGO and Virgo design sensitivities. To infer binary parameters from a GW signal we require accurate models of the gravitational waveform as a function of black hole masses, spins, etc. Such waveform models are built from numerical relativity (NR) simulations and/or semianalytical expressions in the inspiral. We investigate the limits of the current waveform models and study at what detector sensitivity these models will yield unbiased parameter inference for loud golden binary black hole systems, what biases we can expect beyond these limits, and what implications such biases will have for GW astrophysics. For 3G detectors we find that the mismatch error for semianalytical models needs to be reduced by at least three orders of magnitude and for NR waveforms by one order of magnitude. We show that typical biases in units of standard deviations for the mass-ratio and effective aligned-spin will be of order unity for 2G design sensitivity and will reach several tens for 3G networks. In addition, we show that for a population of one hundred high mass precessing binary black holes, measurement errors sum up to a sizable population bias, about 10-30 times larger than the sum of 90% credible intervals for chirp mass, mass-ratio, effective aligned, and precessing spin parameters. Furthermore, we demonstrate that the residual signal between the GW data recorded by a detector and the best fit template waveform obtained by parameter inference analyses can have significant signal-to-noise ratio and can lead to Bayes factors as high as 10(11) between a coherent and an incoherent wavelet model for the population events. This coherent power left in the residual could lead to the observation of erroneous deviations from general relativity. To address these issues and be ready to reap the scientific benefits of 3G GW detectors in the 2030s, waveform models that are significantly more physically complete and accurate need to be developed in the next decade along with major advances in efficiency and accuracy of NR codes.