The impact of precession and higher-order multipoles on cosmological inference

Gravitational-wave astronomy presents an exciting opportunity to provide an independent measurement of the expansion rate of the Universe. By combining inferences for the binary component masses and luminosity distances from individual observations, it is possible to infer $H_0$ without direct electromagnetic counterparts or galaxy catalogs. However, this relies on theoretical gravitational-wave models, which are known to be incomplete descriptions of the full predictions of general relativity. Although the accuracy of our models are improving, they are also becoming increasingly expensive as additional phenomena are incorporated. In this work, we demonstrate that there is no significant advantage in including spin-precession and higher-order multipole moments when inferring $H_0$ via the mass spectrum method for current and near-future gravitational-wave event numbers. Even when simulating a population of highly precessing and preferentially asymmetric-mass-ratio binaries, we show that the inferred $H_0$ posterior changes minimally. Using a simpler, less accurate model, achieves comparable $H_0$ estimates with six times less computational cost (on average). Using computationally cheaper models for single event inference may become crucial as thousands of gravitational-wave observations are expected to be detected in the near future.