Constraining the cosmological parameters using gravitational wave observations of massive black hole binaries and statistical redshift information

Space-borne gravitational wave detectors like TianQin are expected to detect gravitational wave signals emitted by the mergers of massive black hole binaries. Luminosity distance information can be obtained from gravitational wave observations, and one can perform cosmological inference if redshift information can also be extracted, which would be straightforward if an electromagnetic counterpart exists. In this paper, we concentrate on the conservative scenario where the electromagnetic counterparts are not available, and comprehensively study if cosmological parameters can be inferred through a statistical approach, utilizing the nonuniform distribution of galaxies as well as the black hole mass-host galaxy bulge luminosity relationship. By adopting different massive black hole binary merger models, and assuming different detector configurations, we conclude that the statistical inference of cosmological parameters is indeed possible. TianQin is expected to constrain the Hubble constant to a relative error of about 4%-7%, depending on the underlying model. The multidetector network of TianQin and LISA can significantly improve the precision of cosmological parameters. In the most favorable model, it is possible to achieve a level of 1.7% with a network of TianQin and LISA. We find that without electromagnetic counterparts, constraints on all other parameters need a larger number of events or more precise sky localization of gravitational wave sources, which can be achieved by the multidetector network or under a favorable model for massive black hole mergers. However, in the optimistic case, where electromagnetic counterparts are available, one can obtain useful constraints on all cosmological parameters in the Lambda cold dark matter cosmology, regardless of the population model. Moreover, we can also constrain the equation of state of the dark energy without the electromagnetic counterparts, and it is even possible to study the evolution of equation of state of the dark energy when the electromagnetic counterparts are observed.