Inference of the cosmological parameters from gravitational waves: application to second generation interferometers

The advanced world-wide network of gravitational waves (GW) observatories is scheduled to begin operations within the current decade. Thanks to their improved sensitivity, they promise to yield a number of detections and thus to open a new observational windows for astronomy and astrophysics. Among the scientific goals that should be achieved, there is the independent measurement of the value of the cosmological parameters, hence an independent test of the current cosmological paradigm. Due to the importance of such task, a number of studies have evaluated the capabilities of GW telescopes in this respect. However, since GW do not yield information about the source redshift, different groups have made different assumptions regarding the means through which the GW redshift can be obtained. These different assumptions imply also different methodologies to solve this inference problem. This work presents a formalism based on Bayesian inference developed to facilitate the inclusion of all assumptions and prior information about a GW source within a single data analysis framework. This approach guarantees the minimisation of information loss and the possibility of including naturally event-specific knowledge (such as the sky position for a Gamma Ray Burst - GW coincident observation) in the analysis. The workings of the method are applied to a specific example, loosely designed along the lines of the method proposed by Schutz in 1986, in which one uses information from wide-field galaxy surveys as prior information for the location of a GW source. I show that combining the results from few tens of observations from a network of advanced interferometers will constrain the Hubble constant $H_0$ to an accuracy of $\sim 4 - 5$% at 95% confidence.