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Gravitational-wave signals from binary neutron star coalescences carryinformation about the star's equation of state in their tidal signatures. Amajor issue in the inference of the tidal parameters (or directly of theequation of state) is the systematic error introduced by the waveformapproximants. We use a bottom-up approach based on gauge-invariant phaseanalysis and the Fisher information matrix to investigate waveform systematicsand help identifying biases in parameter estimation. A mock analysis of 15different binaries indicates that systematics in current waveform modelsdominate over statistical errors at signal-to-noise ratio (SNR) ${\gtrsim} 80$.This implies biases in the inference of the reduced tidal parameter that areare larger than the statistical $90\%$ credible-intervals. For example, whilethe neutron-star radius could be constrained at ${\sim} 5\%$ level at SNR 80,systematics can be at the ${\sim} 10\%$ level. We apply our approach toGW170817 (SNR ${\sim}30$) and confirm that no significant systematic effectsare present. Using an optimal frequency range for the analysis, we estimate aneutron-star radius of $12.5^{+1.1}_{-1.8}\,$km. The latter is consistent withan electromagnetic-informed prior and the recent NICER measurement. ExploringSNR ${\gtrsim}100$ in view of third-generation detectors, we find that all thecurrent waveform models lead to differences of at least 1-sigma in theinference of the reduced tidal parameter (for any value of the latter). Weconclude that current waveform models, including those from numericalrelativity, are insufficient to infer the equation of state in the loudest (andpotentially most informative) events that will be observed by advanced andthird generation detectors.

Waveform systematics in the gravitational-wave inference of tidal parameters and equation of state from binary neutron star signals