Combining Probes of Large-Scale Structure with CosmoLike

TL;DR

The paper introduces CosmoLike v1.0, a coherent framework to jointly analyze six second-order cosmological probes (from galaxy position, shear, and magnification) with full cross-covariances and non-Gaussian corrections via a halo-model trispectrum. It extends the COSEBIs data-compression approach to all probes, enabling efficient, E/B-separated summaries of the information, and forecasts constraints for DES-like surveys using a five-parameter cosmology plus ten bias/nuisance parameters. The results show that including magnification and cross-probes improves parameter constraints and that accurate covariance modeling is essential for reliable likelihood contours; null-tests based on shear–magnification degeneracies offer powerful tools to identify data contaminations. The work also highlights self-calibration of bias/correlation parameters and outlines future extensions to tomography and more detailed nuisance modeling, such as HOD priors and baryonic effects.

Abstract

Developing accurate analysis techniques to combine various probes of cosmology is essential to tighten constraints on cosmological parameters and to check for inconsistencies in our model of the Universe. In this paper we develop a joint analysis framework for six different second-order statistics calculated from three tracers of the dark matter density field, namely galaxy position, shear, and magnification. We extend a data compression scheme developed in the context of shear-shear statistics (the so-called COSEBIs) to the other five second-order statistics, thereby significantly reducing the number of data points in the joint data vector. We use CosmoLike, a newly developed software framework for joint likelihood analyses, to forecast parameter constraints for the Dark Energy Survey (DES). The simulated MCMCs cover a five dimensional cosmological parameter space comparing the information content of the individual probes to several combined probes (CP) data vectors. Given the significant correlations of these second-order statistics we model all cross terms in the covariance matrix; furthermore we go beyond the Gaussian covariance approximation and use the halo model to include higher order correlations of the density field. We find that adding magnification information (including cross probes with shear and clustering) noticeably increases the information content and that the correct modeling of the covariance (i.e., accounting for non-Gaussianity and cross terms) is essential for accurate likelihood contours from the CP data vector. We also identify several nulltests based on the degeneracy of magnification and shear statistics which can be used to quantify the contamination of data sets by astrophysical systematics and/or calibration issues.

Figures (6)

• Figure 1: Schematic illustration of the modeling of the CP COSEBIs data vector for a given cosmology.
• Figure 2: Schematic illustration of the modeling of the joint COSEBIs covariance for a given cosmology.
• Figure 3: Full (Gaussian+Non-Gaussian) COSEBIs correlation matrix. Since we assume five modes for each of the six probes our data vector contains 30 data points, hence the covariance is 30 $\times$ 30. We indicate the corresponding auto-covariance block matrices in the plots.
• Figure 4: Likelihood analysis in five-dimensional cosmological parameter space as described in the text. We show the 68% credible regions for four different likelihood analyses, i.e. individual probes of cosmic shear, galaxy-galaxy lensing and galaxy clustering, compared to a joint analysis of all three probes (see legend for details).
• Figure 5: Likelihood analysis in four dimensional cosmological parameter space. We show the 68% credible regions and marginalize over the all other parameters not shown in a given panel. We compare CP analyses with and without magnification (Black/solid and red/dashed, respectively). For the full six probe data vector $\mathbf E=(\mathbf E^{\gamma \gamma}$, $\mathbf E^{\mu \mu}$, $\mathbf E^{g g}$, $\mathbf E^{\gamma \mu}$, $\mathbf E^{\gamma g}$, $\mathbf E^{\mu g})$) we also show the difference when using Gaussian instead of Non-Gaussian covariances (blue/dot-dashed and black/solid, respectively).