Cosmology and modified gravitational wave propagation from binary black hole population models

A joint hierarchical Bayesian analysis of the binary black hole (BBH) mass function, merger rate evolution, and cosmological parameters can be used to extract information on both the cosmological and population parameters. We extend this technique to include the effect of modified gravitational wave (GW) propagation. We discuss the constraints on the parameter Xi(0) that describe this phenomenon [with Xi(0) = 1 in general relativity (GR)] using the data from the third gravitational wave transient catalog. We find the constraints Xi(0) = 1.2(-0.7)(+0.7) with a flat prior on Xi(0), and Xi(0) = 1.0(-0.8)(+0.4) with a prior uniform in log Xi(0) (68% C.L., maximum posterior and highest-density interval), which only rely on the presence of a feature in the BBH mass distribution around similar to 30-45 M-circle dot and are robust to whether or not the event GW190521 is considered an outlier of the population. We then study in more detail the effects of modified GW propagation on population and cosmological analyses for LIGO/Virgo at design sensitivity. We find that, for a given data-taking period, the relative error Delta Xi(0)/Xi(0) has a significant dependence on the fiducial value of Xi(0), since the latter has a strong influence on the detection rate. For five years of data, the accuracy ranges from similar to 10% on Xi(0 )when Xi(0) = 1 to Delta Xi(0)/Xi(0) similar to 20% for Xi(0) = 1.8, which represents a large deviation from GR, still consistent with current limits and predicted by viable cosmological models. For the Hubble parameter, we forecast an accuracy of Delta H-0/H-0 similar to 20% and an accuracy on H(z) of similar to 7% at a pivot redshift z(*) similar to 0.8; this updates the results found in previous studies, by making use of a population model compatible with current observations, and is about a factor 2 worse, in twice the observing time. We finally show that, if nature is described by a modified gravity theory with a large deviation from the GR value Xi(0) = 1, such as Xi(0) = 1.8, analyzing the data assuming GR produces a significant bias in the inferred values of the mass scales, Hubble constant, and particularly the BBH merger rate.

Automated summary

A hierarchical Bayesian analysis is used to extract information on cosmological and population parameters of binary black holes (BBH), with a focus on modified gravitational wave (GW) propagation effects. By analyzing data from the third gravitational wave transient catalog, constraints on the parameter Xi(0) describing this phenomenon are found. The study also examines the impact of modified GW propagation on population and cosmological analyses, showing a significant dependence of accuracy on the fiducial value of Xi(0).