The cosmological analysis of X-ray cluster surveys: VI. Inference based on analytically simulated observable diagrams

TL;DR

This paper introduces a neural network-based likelihood-free inference method to extract cosmological parameters from X-ray galaxy cluster surveys using observable data alone, bypassing traditional scaling relation uncertainties.

Contribution

It presents a novel simulation-based inference approach employing CNNs and neural density estimation to directly infer cosmological parameters from observable cluster data without relying on scaling relations.

Findings

Achieves 15.2% error for Ω_m and 10.0% for σ_8 on 1000 deg² survey

Reduces errors to 9.6% for Ω_m and 5.6% for σ_8 on 10000 deg² survey

Demonstrates bias-free cosmological inference from observable data alone

Abstract

The number density of galaxy clusters across mass and redshift has been established as a powerful cosmological probe. Cosmological analyses with galaxy clusters traditionally employ scaling relations. However, many challenges arise from this approach as the scaling relations are highly scattered, may be ill-calibrated, depend on the cosmology, and contain many nuisance parameters with low physical significance. In this paper, we use a simulation-based inference method utilizing artificial neural networks to optimally extract cosmological information from a shallow X-ray survey of galaxy clusters, solely using count rates (CR), hardness ratios (HR), and redshifts. This procedure enables us to conduct likelihood-free inference of cosmological parameters $\Omega_{\mathrm{m}}$ and $\sigma_8$. We analytically generate simulations of galaxy cluster distribution in a CR, HR space in multiple redshift bins based on totally random combinations of cosmological and scaling relation parameters. We train Convolutional Neural Networks (CNNs) to retrieve the cosmological parameters from these simulations. We then use neural density estimation (NDE) neural networks to predict the posterior probability distribution of $\Omega_{\mathrm{m}}$ and $\sigma_8$ given an input galaxy cluster sample. The 1 $\sigma$ errors of our density estimator on one of the target testing simulations are 1000 deg$^2$: 15.2% for $\Omega_{\mathrm{m}}$ and 10.0% for $\sigma_8$; 10000 deg$^2$: 9.6% for $\Omega_{\mathrm{m}}$ and 5.6% for $\sigma_8$. We also compare our results with Fisher analysis. We demonstrate, as a proof of concept, that it is possible to calculate cosmological predictions of $\Omega_{\mathrm{m}}$ and $\sigma_8$ from a galaxy cluster population without explicitly computing cluster masses and even, the scaling relation coefficients, thus avoiding potential biases resulting from such a procedure. [abridged]