Cosmological inference using only gravitational wave observations of binary neutron stars

Gravitational waves emitted during the coalescence of binary neutron star systems are self- calibrating signals. As such, they can provide a direct measurement of the luminosity distance to a source without the need for a cross-calibrated cosmic distance-scale ladder. In general, how- ever, the corresponding redshift measurement needs to be obtained via electromagnetic observations since it is totally degenerate with the total mass of the system. Nevertheless, Fisher matrix studies have shown that, if information about the equation of state of the neutron stars is available, it is possible to extract redshift information from the gravitational wave signal alone. Therefore, measuring the cosmological parameters in pure gravitational-wave fashion is possible. Furthermore, the huge number of sources potentially observable by the Einstein Telescope has led to speculations that the gravitational wave measurement is potentially competitive with traditional methods. The Einstein Telescope is a conceptual study for a third generation gravitational wave detector which is designed to yield 103 − 107 detections of binary neutron star systems per year. This study presents the first Bayesian investigation of the accuracy with which the cosmological parameters can be measured using information coming only from the gravitational wave observations of binary neutron star systems by Einstein Telescope. We find, by direct simulation of 103 detections of binary neutron stars, that, within our simplifying assumptions, H0, Ωm, ΩΛ, w0 and w1 can be measured at the 95% level with an accuracy of ∼ 8%,65%,39%,80% and 90%, respectively. We also find, by extrapolation, that a measurement accuracy comparable with current measurements by Planck is possible if the number of gravitational wave events observed is O(10^{6−7}).We conclude that, while not competitive with electro-magnetic missions in terms of significant digits, gravitational wave alone are capable of providing a complementary determination of the dynamics of the Universe.