Cosmology in the Einstein Telescope era: comparing traditional and simulation-based methods for population inference

The next generation of gravitational wave detectors, such as the Einstein Telescope, will observe orders of magnitude more binary black hole mergers than current facilities. The new analysis still awaits peer review, but it already lays out the central claim clearly.

It is relevant because cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. The next generation of gravitational wave detectors, such as the Einstein Telescope (ET), will observe orders of magnitude more binary black hole mergers than current facilities. Most of these events will lack an electromagnetic counterpart, also known as dark siren events, yet will still enable percent-level cosmological constraints.

However, the likelihood traditionally used in Hierarchical Bayesian Inference (HBI) for population-level analyses becomes computationally prohibitive as the size of dark siren. In this work we compare HBI against simulation-based inference (SBI) as a scalable alternative for cosmological population inference in the ET era.

Studying a proof-of-concept example of a mock ET inference, we build a catalogue of $O(10^4)$ binary black hole events, then perform inference on the Hubble constant $H_0$ and. We find excellent agreement between the two approaches, with SBI reproducing the HBI posteriors to high accuracy, while requiring orders of magnitude less computation once the.

We further demonstrate that SBI extends straightforwardly to a joint cosmology-plus-astrophysics analysis, simultaneously constraining $(H_0, Ω_m)$ together with the parameters of. Our results indicate that SBI is a promising and scalable tool for population inference with third-generation GW detectors.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

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Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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