Integrated approach to cosmology: Combining CMB, large-scale structure and weak lensing

Recent observational progress has led to the establishment of the standard $\Lambda$CDM model for cosmology. This development is based on different cosmological probes that are usually combined through their likelihoods at the latest stage in the analysis. We implement here an integrated scheme for cosmological probes, which are combined in a common framework starting at the map level. This treatment is necessary as the probes are generally derived from overlapping maps and are thus not independent. It also allows for a thorough test of the cosmological model and of systematics through the consistency of different physical tracers. As a first application, we combine current measurements of the Cosmic Microwave Background (CMB) from the Planck satellite, and galaxy clustering and weak lensing from SDSS. We consider the spherical harmonic power spectra of these probes including all six auto- and cross-correlations along with the associated full Gaussian covariance matrix. This provides an integrated treatment of different analyses usually performed separately including CMB anisotropies, cosmic shear, galaxy clustering, galaxy-galaxy lensing and the Integrated Sachs-Wolfe (ISW) effect with galaxy and shear tracers. We derive constraints on $\Lambda$CDM parameters that are compatible with existing constraints and highlight tensions between data sets, which become apparent in this integrated treatment. We discuss how this approach provides a complete and powerful integrated framework for probe combination and how it can be extended to include other tracers in the context of current and future wide field cosmological surveys.Comment: 29 pages, 19 figures, 3 tables, to appear in PRD, updated following referee's comments including small changes in result

Cosmic Shear with Einstein Rings

We explore a new technique to measure cosmic shear using Einstein rings. In Birrer et al. (2017), we showed that the detailed modelling of Einstein rings can be used to measure external shear to high precision. In this letter, we explore how a collection of Einstein rings can be used as a statistical probe of cosmic shear. We present a forecast of the cosmic shear information available in Einstein rings for different strong lensing survey configurations. We find that, assuming that the number density of Einstein rings in the COSMOS survey is representative, future strong lensing surveys should have a cosmological precision comparable to the current ground based weak lensing surveys. We discuss how this technique is complementary to the standard cosmic shear analyses since it is sensitive to different systematic and can be used for cross-calibration.Comment: 4 pages, 1 figure, 1 table. ApJL accepte

Integrated cosmological probes: Concordance quantified

Assessing the consistency of parameter constraints derived from different cosmological probes is an important way to test the validity of the underlying cosmological model. In an earlier work [Nicola et al., 2017], we computed constraints on cosmological parameters for $\Lambda$CDM from an integrated analysis of CMB temperature anisotropies and CMB lensing from Planck, galaxy clustering and weak lensing from SDSS, weak lensing from DES SV as well as Type Ia supernovae and Hubble parameter measurements. In this work, we extend this analysis and quantify the concordance between the derived constraints and those derived by the Planck Collaboration as well as WMAP9, SPT and ACT. As a measure for consistency, we use the Surprise statistic [Seehars et al., 2014], which is based on the relative entropy. In the framework of a flat $\Lambda$CDM cosmological model, we find all data sets to be consistent with one another at a level of less than 1$\sigma$. We highlight that the relative entropy is sensitive to inconsistencies in the models that are used in different parts of the analysis. In particular, inconsistent assumptions for the neutrino mass break its invariance on the parameter choice. When consistent model assumptions are used, the data sets considered in this work all agree with each other and $\Lambda$CDM, without evidence for tensions.Comment: 17 pages, 4 figures, 2 tables, updated following referee's comments, now includes discussion of the Riess et al., 2016 Hubble parameter measurement, matches version accepted by JCA

Cross-correlating 21 cm and galaxy surveys: implications for cosmology and astrophysics

We forecast astrophysical and cosmological parameter constraints from synergies between 21 cm intensity mapping and wide field optical galaxy surveys (both spectroscopic and photometric) over $z \sim 0-3$. We focus on the following survey combinations in this work: (i) a CHIME-like and DESI-like survey in the northern hemisphere, (ii) an LSST-like and SKA I MID-like survey and (ii) a MeerKAT-like and DES-like survey in the southern hemisphere. We work with the $\Lambda$CDM cosmological model having parameters $\{h, \Omega_m, n_s, \Omega_b, \sigma_8\}$, parameters $v_{c,0}$ and $\beta$ representing the cutoff and slope of the HI-halo mass relation in the previously developed HI halo model framework, and a parameter $Q$ that represents the scale dependence of the optical galaxy bias. Using a Fisher forecasting framework, we explore (i) the effects of the HI and galaxy astrophysical uncertainties on the cosmological parameter constraints, assuming priors from the present knowledge of the astrophysics, (ii) the improvements on astrophysical constraints over their current priors in the three configurations considered, (ii) the tightening of the constraints on the parameters relative to the corresponding HI auto-correlation surveys alone.Comment: 9 pages, 5 figures, 2 tables; accepted for publication in MNRA

Consistency tests in cosmology using relative entropy

With the high-precision data from current and upcoming experiments, it becomes increasingly important to perform consistency tests of the standard cosmological model. In this work, we focus on consistency measures between different data sets and methods that allow us to assess the goodness of fit of different models. We address both of these questions using the relative entropy or Kullback-Leibler (KL) divergence [Kullback et al., 1951]. First, we revisit the relative entropy as a consistency measure between data sets and further investigate some of its key properties, such as asymmetry and path dependence. We then introduce a novel model rejection framework, which is based on the relative entropy and the posterior predictive distribution. We validate the method on several toy models and apply it to Type Ia supernovae data from the JLA and CMB constraints from Planck 2015, testing the consistency of the data with six different cosmological models.Comment: 31 pages, 10 figures, 4 tables, updated following referee's comments, matches version accepted by JCA

Image processing challenges in weak gravitational lensing

The field of weak gravitational lensing, which measures the basic properties of the Universe by studying the way that light from distant galaxies is perturbed as it travels towards us, is a very active field in astronomy. This short article presents a broad overview of the field, including some of the important questions that cosmologists are trying to address, such as understanding the nature of dark energy and dark matter. To do this, there is an increasing feeling within the weak lensing community that other disciplines, such as computer science, machine learning, signal processing and image processing, have the expertise that would bring enormous advantage if channelled into lensing studies. To illustrate this point, the article below outlines some of the key steps in a weak lensing analysis chain. The challenges are distinct at each step, but each could benefit from ideas developed in the signal processing domain. This article also gives a brief overview of current and planned lensing experiments that will soon bring about an influx of data sets that are substantially larger than those analysed to date. It is, therefore, inevitable that current techniques are likely to be insufficient, thus leading to an exciting era where new methods will become crucial for the continued success of the field.Comment: Conference Proceeding for ICIP 2011 (IEEE). 4 pages and 3 figure