Blinded Mock Data Challenge for Gravitational-Wave Cosmology-I: Assessing the Robustness of Methods Using Binary Black Holes Mass Spectrum

Gravitational Wave (GW) sources are standard sirens that provide an independent way to map the cosmic expansion history by combining with an independent redshift measurement either from an electromagnetic counterpart for a bright siren or using different statistical techniques for dark sirens. In this analysis, we perform the first Blinded Mock Data Challenge (\texttt{Blinded-MDC}) to test the robustness in inferring the value of Hubble constant $H_0$ for a dark siren technique which depends on astrophysical mass distribution of Binary Black Holes (BBHs). We have considered different analysis setups for the \texttt{Blinded-MDC} to test both statistical and systematic uncertainties and demonstrate the capabilities in inferring $H_0$ with detector sensitivity as per the fourth observation run of LIGO-Virgo-KAGRA. We find that when the astrophysical population of BBHs matches with the underlying assumption of the model, a cosmological pipeline can recover the injected parameters using the observed mass distribution. However, when the mock mass distribution of the astrophysical population depends slightly on redshift and one is ignorant about it in analyzing the data, it can cause a systematic discrepancy in the inferred value of $H_0$ by about $1.5\sigma$, above the statistical fluctuations due to noise and a limited number of events. In the future, elaborate studies will be required to mitigate systematic uncertainties due to unknown astrophysical complexities. This MDC framework sets the road map for inspecting the precision and accuracy of standard siren cosmology and provides the first insight into the robustness of the population-dependent cosmology inference in a blinded analysis setup.