Likelihoodfree Forward Modeling for Cluster Weak Lensing and Cosmology
Abstract
Likelihoodfree inference provides a rigorous approach to performing Bayesian analysis using forward simulations only. The main advantage of likelihoodfree methods is their ability to account for complex physical processes and observational effects in forward simulations. Here we explore the potential of likelihoodfree forward modeling for Bayesian cosmological inference using the redshift evolution of the cluster abundance combined with weaklensing mass calibration. We use two complementary likelihoodfree methods, namely Approximate Bayesian Computation (ABC) and DensityEstimation LikelihoodFree Inference (DELFI), to develop an analysis procedure for the inference of the cosmological parameters (Ω_{m}, σ _{8}) and the mass scale of the survey sample. Adopting an eROSITAlike selection function and a 10% scatter in the observablemass relation in a flat ΛCDM cosmology with Ω_{m} = 0.286 and σ _{8} = 0.82, we create a synthetic catalog of observableselected NavarroFrenkWhite clusters in a survey area of 50 deg^{2}. The stacked tangential shear profile and the number counts in redshift bins are used as summary statistics for both methods. By performing a series of forward simulations, we obtain convergent solutions for the posterior distribution from both methods. We find that ABC recovers broader posteriors than DELFI, especially for the Ω_{m} parameter. For a weaklensing survey with a source density of n _{g} = 20 arcmin^{2}, we obtain posterior constraints on ${S}_{8}={\sigma }_{8}{\left({{\rm{\Omega }}}_{{\rm{m}}}/0.3\right)}^{0.3}$ of 0.836 ± 0.032 and 0.810 ± 0.019 from ABC and DELFI, respectively. The analysis framework developed in this study will be particularly powerful for cosmological inference with ongoing cluster cosmology programs, such as the XMMXXL survey and the eROSITA allsky survey, in combination with widefield weaklensing surveys.
 Publication:

The Astrophysical Journal
 Pub Date:
 February 2022
 DOI:
 10.3847/15384357/ac3d33
 arXiv:
 arXiv:2109.09741
 Bibcode:
 2022ApJ...925..145T
 Keywords:

 1797;
 1146;
 584;
 1900;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 Version accepted by ApJ, with textual changes to improve clarity (e.g., more details on the simulation procedure added in Section 3