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

Abstract

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.

Figures (9)

• Figure 1: Illustration of a binary with Left: spin angular momentum $\hat{\mathbf{S}} = \hat{\mathbf{S}}_{1} + \hat{\mathbf{S}}_{2}$ aligned with the orbital angular momentum $\hat{\mathbf{L}}$, and Right: $\hat{\mathbf{S}}$ misaligned with $\hat{\mathbf{L}}$. When $\hat{\mathbf{S}}$ is misaligned with $\hat{\mathbf{L}}$ the binary undergoes the general relativistic phenomenon of spin-induced orbital precession: both $\hat{\mathbf{S}}$ and $\hat{\mathbf{L}}$ precess around the direction of the total angular momentum $\hat{\mathbf{J}} = \hat{\mathbf{L}} + \hat{\mathbf{S}}$ leaving visible amplitude modulations in the emitted Apostolatos:1994mx. The dashed black line shows an instantaneous snapshot of the orbital plane. The dotted black line in the Right panel indicates the path of $\hat{\mathbf{L}}$ as it precesses around $\hat{\mathbf{J}}$, and the dotted black line shows a snapshot of the orbital plane when $\hat{\mathbf{L}}$ has partially rotated around $\hat{\mathbf{J}}$.
• Figure 2: Two-dimensional marginalized posterior distributions for the inferred Top: luminosity distance, $d_{\mathrm{L}}$, and inclination angle, $\theta_{\mathrm{JN}}$ and Bottom: chirp mass $\mathcal{M}$, and mass ratio $q$ for three simulated signals injected into a three-detector network operating at their design sensitivities for the fourth GW observing run O4PSD. All simulated signals were produced with XPHM. Contours show the 90% credible interval, and different colours represent posterior distributions obtained with different models, as indicated in the legend. The black cross hairs show the injected value. The Left panel shows an analysis of an injection with no detectable precession and higher-order multipole moments, the Middle panel shows an analysis of an injection with detectable precession, and the Right panel shows an analysis of an injection with detectable higher-order multipole moments. Since these injections were analysed in idealised Gaussian noise, the peak of the posterior will not always lie at the true value, even when the model used for the injection and recovery is the same.
• Figure 3: A subset of the cosmological and population parameters obtained when analyzing the GWTC-3 catalog of . The posteriors are colored according to the waveform assumed for the single-event PE. The hyperparameters were selected since they are either of cosmological interest ($H_0$), correlate strongly with $H_0$ ($\gamma$, $m_{\rm max}$) or are most affected by the choice of waveform model ($m_{\rm max}$).
• Figure 4: In grey we show the properties of 100,000 binaries drawn from a highly spinning, preferentially asymmetric component mass population of . In orange we show the 80 randomly chosen injections that have SNR $> 12$, analysed in Sec. \ref{['sec:simulation']}.
• Figure 5: A subset of the cosmological and population parameters that are most affected by the choice of waveform model when analysing 80 signals drawn from a fiducial population with high spins and preferentially asymmetric-mass binaries. The posteriors are colored according to the waveform assumed for the single-event PE and the black cross hairs show the true population values.