Galaxy cluster count cosmology with simulation-based inference

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Volume 708 (April 2026)

A&A, 708 (2026) A260

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Table 4.

Definition of six pipeline parameters, their mock UNIT1i values (true values), and their inferred values obtained through SBI.

Parameters	Definitions	UNIT1i value	Fitted value	Stat error	Sys error
Ω_m	Matter density as a fraction of critical density	0.309	0.330	$_{- 0.048}^{+ 0.031}$ $Mathematical equation: $ ^{+0.031}_{-0.048} $$	$_{- 0.067}^{+ 0.042}$ $Mathematical equation: $ ^{+0.042}_{-0.067} $$
σ₈	Amplitude of density fluctuations on a scale of 8 Mpc/h	0.815	0.784	$_{- 0.030}^{+ 0.030}$ $Mathematical equation: $ ^{+0.030}_{-0.030} $$	$_{- 0.053}^{+ 0.073}$ $Mathematical equation: $ ^{+0.073}_{-0.053} $$
H₀	Hubble constant	67.74	68.2	$_{- 1.9}^{+ 1.4}$ $Mathematical equation: $ ^{+1.4}_{-1.9} $$	$_{- 0.921}^{+ 2.193}$ $Mathematical equation: $ ^{+2.193}_{-0.921} $$
A_lm	Mass-luminosity slope	1.620	1.730	$_{- 0.29}^{+ 0.29}$ $Mathematical equation: $ ^{+0.29}_{-0.29} $$	$_{- 0.213}^{+ 0.219}$ $Mathematical equation: $ ^{+0.219}_{-0.213} $$
B_lm	Mass-luminosity normalization	−0.499	−0.608	$_{- 0.1}^{+ 0.089}$ $Mathematical equation: $ ^{+0.089}_{-0.1} $$	$_{- 0.072}^{+ 0.071}$ $Mathematical equation: $ ^{+0.071}_{-0.072} $$
σ_lm	Mass-luminosity scatter	0.809	0.705	$_{- 0.071}^{+ 0.071}$ $Mathematical equation: $ ^{+0.071}_{-0.071} $$	$_{- 0.135}^{+ 0.130}$ $Mathematical equation: $ ^{+0.130}_{-0.135} $$

Notes. The inferred values were obtained from a run using flat priors for each parameter and a uniform proposal distribution for training the model, performed on a fiducial area of 1000 deg². Separate columns show the statistical and systematic uncertainties contributing to the total error budget. The systematic uncertainties were obtained by adding in quadrature the contributions from the halo mass function, cosmic variance, and mass–temperature normalization, as detailed in Sect. 5.3. The UNIT1i values for A_lm, B_lm, and σ_lm were fit from the mock.

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