Hierarchical Cosmic Shear Power Spectrum Inference

We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear field and its (tomographic) power spectra. Inference of the shear power spectrum is a powerful intermediate product for a cosmic shear analysis, since it requires very few model assumptions and can be used to perform inference on a wide range of cosmological models \emph{a posteriori} without loss of information. We show that joint posterior for the shear map and power spectrum can be sampled effectively by Gibbs sampling, iteratively drawing samples from the map and power spectrum, each conditional on the other. This approach neatly circumvents difficulties associated with complicated survey geometry and masks that plague frequentist power spectrum estimators, since the power spectrum inference provides prior information about the field in masked regions at every sampling step. We demonstrate this approach for inference of tomographic shear $E$-mode, $B$-mode and $EB$-cross power spectra from a simulated galaxy shear catalogue with a number of important features; galaxies distributed on the sky and in redshift with photometric redshift uncertainties, realistic random ellipticity noise for every galaxy and a complicated survey mask. The obtained posterior distributions for the tomographic power spectrum coefficients recover the underlying simulated power spectra for both $E$- and $B$-modes.Comment: 16 pages, 8 figures, accepted by MNRA

Simulating weak gravitational lensing for cosmology

This thesis will present a new cosmic shear analysis pipeline SUNGLASS (Simulated UNiverses for Gravitational Lensing Analysis and Shear Surveys). SUNGLASS is a pipeline that rapidly generates simulated universes for weak lensing and cosmic shear analysis. The pipeline forms suites of cosmological N-body simulations and performs tomographic cosmic shear analysis using a novel line-of-sight integration through the simulations while saving the particle lightcone information. Galaxy shear and convergence catalogues with realistic 3-D galaxy redshift distributions are produced for the purposes of testing weak lensing analysis techniques and generating covariance matrices for data analysis and cosmological parameter estimation. This thesis presents a suite of fast medium-resolution simulations with shear and convergence maps for a generic 100 square degree survey out to a redshift of z = 1.5, with angular power spectra agreeing with the theoretical expectations to better than a few percent accuracy up to ℓ = 103 for all source redshifts up to z = 1.5 and wavenumbers up to ℓ = 2000 for source redshifts z ≥ 1.1. A two-parameter Gaussian likelihood analysis of Ωm and σ8 is also performed on the suite of simulations for a 2-D weak lensing survey, demonstrating that the cosmological parameters are recovered from the simulations and the covariance matrices are stable for data analysis, with negligible bias. An investigation into the accuracy of traditional Fisher matrix calculations is presented. Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this thesis, the loss of information is quantified by comparing näıve Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of the suite of mock weak lensing catalogues derived from the SUNGLASS pipeline, for 2-D and tomographic shear analyses of a Euclid-like survey. In both cases the 68% confidence area of the Ωm − σ8 plane is found to increase by a factor 5. However, the marginal errors increase by just 20 to 40%. A new method is proposed to model the effects of non-linear shear-power mode-coupling in the Fisher Matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. The findings in this thesis show that this approximation can reproduce the 68% confidence regions of the full Maximum Likelihood analysis in the Ωm − σ8 plane to high accuracy for both 2-D and tomographic weak lensing surveys. Finally, three multi-parameter analyses of (Ωm, σ8, ns), (Ωm, σ8, ns, ΩΛ)and (Ωm, σ8, h, ns, w0, wa) are performed to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The multi-parameter volumes of the 1σ error contours for the six-parameter non-linear Fisher analysis are consistently larger than for the Gaussian case, and the shape of the 68% confidence volume is modified. These results strongly suggest that future Fisher Matrix estimates of cosmological parameter accuracies should include mode-coupling effects

Predicting H{\alpha} emission line galaxy counts for future galaxy redshift surveys

Knowledge of the number density of H$\alpha$ emitting galaxies is vital for assessing the scientific impact of the Euclid and WFIRST missions. In this work we present predictions from a galaxy formation model, Galacticus, for the cumulative number counts of H$\alpha$-emitting galaxies. We couple Galacticus to three different dust attenuation methods and examine the counts using each method. A $\chi^2$ minimisation approach is used to compare the model predictions to observed galaxy counts and calibrate the dust parameters. We find that weak dust attenuation is required for the Galacticus counts to be broadly consistent with the observations, though the optimum dust parameters return large values for $\chi^2$, suggesting that further calibration of Galacticus is necessary. The model predictions are also consistent with observed estimates for the optical depth and the H$\alpha$ luminosity function. Finally we present forecasts for the redshift distributions and number counts for two Euclid-like and one WFIRST-like survey. For a Euclid-like survey with redshift range $0.9\leqslant z\leqslant 1.8$ and H$\alpha+{\rm [NII]}$ blended flux limit of $2\times 10^{-16}{\rm erg}\,{\rm s}^{-1}\,{\rm cm}^{-2}$ we predict a number density between 3900--4800 galaxies per square degree. For a WFIRST-like survey with redshift range $1\leqslant z\leqslant 2$ and blended flux limit of $1\times 10^{-16}{\rm erg}\,{\rm s}^{-1}\,{\rm cm}^{-2}$ we predict a number density between 10400--15200 galaxies per square degree.Comment: 21 pages (including appendix), 12 figures, 6 tables. Accepted b

Complementary Cosmological Simulations

Cosmic variance limits the accuracy of cosmological N-body simulations, introducing bias in statistics such as the power spectrum, halo mass function, or the cosmic shear. We provide new methods to measure and reduce the effect of cosmic variance in existing and new simulations. We run pairs of simulations using phase shifted initial conditions with matching amplitudes. We set the initial amplitudes of the Fourier modes to ensure that the average power spectrum of the pair is equal to the cosmic mean power spectrum from linear theory. The average power spectrum of a pair of such simulations remains consistent with the estimated non-linear spectra of the state-of-the-art methods even at late times. We also show that the effect of cosmic variance on any analysis involving a cosmological simulation can be estimated by using the complementary pair of the original simulation. To demonstrate the effectiveness of our novel technique, we simulated a complementary pair of the original Millennium run and quantified the degree to which cosmic variance affected its the power spectrum. The average power spectrum of the original and complementary Millennium simulation was able to directly resolve the baryon acoustic oscillation features.Comment: 7 pages, 4 figures, submitted to Astronomy & Astrophysics (A&A

Constraining cosmology with shear peak statistics: tomographic analysis

International audienceThe abundance of peaks in weak gravitational lensing maps is a potentially powerful cosmological tool, complementary to measurements of the shear power spectrum. We study peaks detected directly in shear maps, rather than convergence maps, an approach that has the advantage of working directly with the observable quantity, the galaxy ellipticity catalog. Using large numbers of numerical simulations to accurately predict the abundance of peaks and their covariance, we quantify the cosmological constraints attainable by a large-area survey similar to that expected from the Euclid mission, focusing on the density parameter, Ωm, and on the power spectrum normalization, σ8, for illustration. We present a tomographic peak counting method that improves the conditional (marginal) constraints by a factor of 1.2 (2) over those from a two-dimensional (i.e., non-tomographic) peak-count analysis. We find that peak statistics provide constraints an order of magnitude less accurate than those from the cluster sample in the ideal situation of a perfectly known observable-mass relation; however, when the scaling relation is not known a priori, the shear-peak constraints are twice as strong and orthogonal to the cluster constraints, highlighting the value of using both clusters and shear-peak statistics

Report from the Tri-Agency Cosmological Simulation Task Force

The Tri-Agency Cosmological Simulations (TACS) Task Force was formed when Program Managers from the Department of Energy (DOE), the National Aeronautics and Space Administration (NASA), and the National Science Foundation (NSF) expressed an interest in receiving input into the cosmological simulations landscape related to the upcoming DOE/NSF Vera Rubin Observatory (Rubin), NASA/ESA's Euclid, and NASA's Wide Field Infrared Survey Telescope (WFIRST). The Co-Chairs of TACS, Katrin Heitmann and Alina Kiessling, invited community scientists from the USA and Europe who are each subject matter experts and are also members of one or more of the surveys to contribute. The following report represents the input from TACS that was delivered to the Agencies in December 2018.Comment: 36 pages, 3 figures. Delivered to NASA, NSF, and DOE in Dec 201

Galaxy alignments: An overview

The alignments between galaxies, their underlying matter structures, and the cosmic web constitute vital ingredients for a comprehensive understanding of gravity, the nature of matter, and structure formation in the Universe. We provide an overview on the state of the art in the study of these alignment processes and their observational signatures, aimed at a non-specialist audience. The development of the field over the past one hundred years is briefly reviewed. We also discuss the impact of galaxy alignments on measurements of weak gravitational lensing, and discuss avenues for making theoretical and observational progress over the coming decade.Comment: 43 pages excl. references, 16 figures; minor changes to match version published in Space Science Reviews; part of a topical volume on galaxy alignments, with companion papers at arXiv:1504.05546 and arXiv:1504.0546

Galaxy alignments: Observations and impact on cosmology

Galaxy shapes are not randomly oriented, rather they are statistically aligned in a way that can depend on formation environment, history and galaxy type. Studying the alignment of galaxies can therefore deliver important information about the physics of galaxy formation and evolution as well as the growth of structure in the Universe. In this review paper we summarise key measurements of galaxy alignments, divided by galaxy type, scale and environment. We also cover the statistics and formalism necessary to understand the observations in the literature. With the emergence of weak gravitational lensing as a precision probe of cosmology, galaxy alignments have taken on an added importance because they can mimic cosmic shear, the effect of gravitational lensing by large-scale structure on observed galaxy shapes. This makes galaxy alignments, commonly referred to as intrinsic alignments, an important systematic effect in weak lensing studies. We quantify the impact of intrinsic alignments on cosmic shear surveys and finish by reviewing practical mitigation techniques which attempt to remove contamination by intrinsic alignments.Comment: 52 pages excl. references, 16 figures; minor changes to match version published in Space Science Reviews; part of a topical volume on galaxy alignments, with companion papers arXiv:1504.05456 and arXiv:1504.0554