Combining cosmological constraints from cluster counts and galaxy clustering

TL;DR

This paper discusses a method to combine cluster counts and galaxy clustering data using the halo model and Bayesian hyperparameters, aiming to improve cosmological constraints from large scale surveys.

Contribution

It introduces a diagrammatic approach to model cross-covariance and extends Bayesian hyperparameters to Poissonian distributions for joint likelihood analysis.

Findings

Developed a diagrammatic method for cross-covariance computation.

Extended Bayesian hyperparameters to Poissonian distributions.

Proposed a joint likelihood framework for combined probes.

Abstract

Present and future large scale surveys offer promising probes of cosmology. For example the Dark Energy Survey (DES) is forecast to detect ~300 millions galaxies and thousands clusters up to redshift ~1.3. I here show ongoing work to combine two probes of large scale structure : cluster number counts and galaxy 2-point function (in real or harmonic space). The halo model (coupled to a Halo Occupation Distribution) can be used to model the cross-covariance between these probes, and I introduce a diagrammatic method to compute easily the different terms involved. Furthermore, I compute the joint non-Gaussian likelihood, using the Gram-Charlier series. Then I show how to extend the methods of Bayesian hyperparameters to Poissonian distributions, in a first step to include them in this joint likelihood.