The Cosmological analysis of X-ray cluster surveys - VII. Bypassing scaling relations with Lagrangian Deep Learning and Simulation-based inference

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Table 3.

Performances of different test statistics with simulation-based model.

Observables used in the summary statistics	FoM	$Δ Ω_{m} (\frac{Δ Ω_{m}}{Ω_{m}})$ $\Delta \Omega_m \ \left( \frac{\Delta \Omega_m}{\Omega_m}\right)$	$Δ σ_{8} (\frac{Δ σ_{8}}{σ_{8}})$ $\Delta \sigma_8 \ \left( \frac{\Delta \sigma_8}{\sigma_8}\right)$
z, CR, HR	17	0.068 (23%)	0.090 (11%)
CR, HR	14	0.076 (25%)	0.11 (14%)
z, CR	10	0.082 (27%)	0.12 (15%)
z	9	0.087 (29%)	0.13 (16%)

Notes. We obtain posteriors from different test statistics, and display the 68% credibility intervals for Ω_m and σ₈, as well as the Figure of merit (FoM = Cov(Ω_m, σ₈)⁻¹). The same parametrisation is used for each test statistics and informative constraints are retrieved. This highlights the universality of our physical modelling based on simulations.

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