Pushing spectral siren cosmology into the third-generation era: a blinded mock data challenge

Gravitational wave (GW) spectral sirens offer a promising method for measuring cosmological parameters using GW data only - without relying on external redshift information such as electromagnetic counterparts or galaxy catalogs - by exploiting distributional features in the population of GW sources. The advent of third-generation detectors like the Einstein Telescope (ET) will provide catalogs three orders of magnitudes larger than current ones, raising questions about the scalability and robustness of existing inference pipelines. We present a blinded mock data challenge that tests three public pipelines with distinct numerical implementations, namely, $\texttt{ICAROGW}$, $\texttt{CHIMERA}$, and $\texttt{pymcpop-gw}$, on simulated ET observations containing the best $\mathcal{O}(10^4)$ binary black hole mergers that can be observed in 1 year. We assess their computational performance, validate their agreement in a blinded setting, and forecast cosmological constraints. We find that, thanks to GPU acceleration, these pipelines can process the events expected from ET within a manageable timeframe. All pipelines recover consistent cosmological and population parameters. Assuming a flat $\Lambda$CDM model, we measure $H(z)$ at $z\sim1.5$ with 2.4% precision, and achieve a mean precision on $H(z)$ of 2.8% across $0.7<z<1.8$ with a catalog of $\sim 12,000$ high-S/N events. This corresponds to joint constraints of $\sim 10$ on $H_0$ and $\sim 26$ on $\Omega_{\rm m,0}$. We also identify the events that contribute mostly to constraining cosmological parameters, showing that low-distance sources near population features drive the constraining power on all cosmological parameters, while higher-distance events primarily constrain $\Omega_{\rm m,0}$. Our results establish a validated, performance-tested framework for spectral siren cosmology in the era of third-generation GW observatories.