Cosmic shear analysis from theory to data

One of the most important challenges in cosmology today is understanding the dark matter and dark energy which composite together 95% of the cosmic energy density of the Universe. Weak gravitational lensing by large scale structures is one of the most promising probes for understanding these components and therefore the Universe. The imaging surveys of the future will cover wider fields of view, more accurate redshift estimations and deeper galaxy images. This will leads to smaller statistical errors and tighter parameter constraints. This increased statistical precision will not be satisfactory, however, unless there are trustworthy and accurate methods to analyse the data in order to extract all the information they can offer. In this thesis I will explore two cosmic shear analysis methods, COSEBIs (Complete Orthogonal Sets of E-/B-Integrals) and PCls (Pseudo Cls). Both of these methods are able to separate gravitational lensing effects (E-modes) from the contaminants (B-modes). A prominent challenge for cosmological surveys is the estimation of accurate data covariances. N-body cosmological simulations are the most common method used for estimating the covariance, but a large number of simulations with high enough resolution have to be run to estimate accurate data covariances. This number grows with the number of data points used in the analysis. Running cosmological simulations is time consuming and expensive. Therefore, data compression is highly desirable for many disciplines. In Chapter 3 I introduce a method that optimally compresses the number of observables according to their sensitivity to the parameters to be estimated. I then apply this method to COSEBIs (Complete Orthogonal Sets of E-/B-Integrals), an analysis method for weak gravitational lensing, and show that the compressed observables are not sensitive to the choice of the input covariance matrix used to define them. In Chapter 4 I set up a blind analysis of CFHTLenS2 , the state-of-the-art weak gravitational lensing survey, using COSEBIs and their compressed version. I present a likelihood analysis to estimate cosmological parameters from the data. This is the first time this form of optimised compression has been applied to data. I will also use tomographic redshift bins with COSEBIs and compressed COSEBIs for the first time. The tightest constraints I find for the best cosmological parameter combination is σ8(Ωm/0.27)0.62 = 0.825+0.033−0.044, which is consistent with previous analysis of CFHTLenS data. In Chapter 5 I employ Gaussian and lognormal simulated shear fields to explore a flat sky Pseudo Cl analysis pipeline which I have developed. Although, shear two-point correlation functions are insensitive to the mask which are always present on galaxy images, their Fourier counterparts, shear power spectra, are biased by them. Therefore, the effects of masking should be considered in Fourier space analysis of weak gravitational lensing data. I use different masks and propagate errors to cosmological parameters using Fisher analysis to explore the limitations and strengths of Pseudo Cl method. In the final Chapter I will conclude that the studies presented in this thesis strongly advocates and prefers the use of the presented methods in Chapters 3 and 4, for any future analysis of weak gravitational lensing data. In addition, the compression method in Chapter 3 can also be applied to other cosmological analysis. And finally to avoid biased results Pseudo Cl analysis for the future surveys have to be performed with the considerations detailed in Chapter 5

Dark Energy Survey Year 1: An independent E/B-mode cosmic shear analysis

We present an independent cosmic shear analysis of the non-cosmological B-mode distortions within the public first year data from the Dark Energy Survey (DES). We find no significant detection of B-modes in a full tomographic analysis of the primary METACALIBRATION shear catalogue. This is in contrast to the secondary IM3SHAPE shear catalogue, where we detect B- modes at a significance of $\sim 3\sigma$ with a pattern that is consistent with the B-mode signature of a repeating additive shear bias across the survey. We use the COSEBIs statistic to cleanly separate the B-modes from the gravitational lensing signal (E-modes). We find good agreement between the measured E-modes and their theoretical expectation given the DES cosmological parameter constraints.Comment: 5 Pages, 2 Figure

Revisiting CFHTLenS cosmic shear: optimal E/B mode decomposition using COSEBIs and compressed COSEBIs

We present a re-analysis of the CFHTLenS weak gravitational lensing survey using Complete Orthogonal Sets of E/B-mode Integrals, known as COSEBIs. COSEBIs provide a complete set of functions to efficiently separate E-modes from B-modes and hence allow for robust and stringent tests for systematic errors in the data. This analysis reveals significant B-modes on large angular scales that were not previously seen using the standard E/B decomposition analyses. We find that the significance of the B-modes is enhanced when the data are split by galaxy type and analysed in tomographic redshift bins. Adding tomographic bins to the analysis increases the number of COSEBIs modes, which results in a less-accurate estimation of the covariance matrix from a set of simulations. We therefore also present the first compressed COSEBIs analysis of survey data, where the COSEBIs modes are optimally combined based on their sensitivity to cosmological parameters. In this tomographic CCOSEBIs analysis, we find the B-modes to be consistent with zero when the full range of angular scales are considered

Flat-sky pseudo-cls analysis for weak gravitational lensing

We investigate the use of estimators of weak lensing power spectra based on a flat-sky implementation of the Pseudo-Cl (PCl) technique, where the masked shear field is transformed without regard for masked regions of sky. This masking mixes power, and E-convergence and B-modes. To study the accuracy of forward-modelling and full-sky power spectrum recovery we consider both large-area survey geometries, and small-scale masking due to stars and a checkerboard model for field-of-view gaps. The power spectrum for the large-area survey geometry is sparsely-sampled and highly oscillatory, which makes modelling problematic. Instead, we derive an overall calibration for large-area mask bias using simulated fields. The effects of small-area star masks can be accurately corrected for, while the checkerboard mask has oscillatory and spiky behaviour which leads to percent biases. Apodisation of the masked fields leads to increased biases and a loss of information. We find that we can construct an unbiased forward-model of the raw PCls, and recover the full-sky convergence power to within a few percent accuracy for both Gaussian and lognormal-distributed shear fields. Propagating this through to cosmological parameters using a Fisher-Matrix formalism, we find we can make unbiased estimates of parameters for surveys up to 1,200 deg$^2$ with 30 galaxies per arcmin$^2$, beyond which the percent biases become larger than the statistical accuracy. This implies a flat-sky PCl analysis is accurate for current surveys but a Euclid-like survey will require higher accuracy.Comment: 25 pages, 14 figure

On constraining Cosmology and the Halo Mass Function with Weak Gravitational Lensing

The discrepancy between the weak lensing (WL) and the {\it Planck} measurements of $S_8$ has been a subject of several studies. These studies tend to show that a suppression of the amplitude of the mass power spectrum $P(k)$ at high $k$ could resolve it. The WL signal at small-scale is sensitive to various effects, such as baryonic effects and intrinsic alignment. The accuracy of $P(k)$ depends on the modelling precision of these effects. A common approach for calculating $P(k)$ relies on a halo model. Amongst the various components necessary for the construction of $P(k)$, the halo mass function (HMF) is an important one. Traditionally, the HMF has been assumed to follow a fixed model. Recent literature shows that baryonic physics, amongst several other factors, could affect the HMF. In this study, we investigate the impact of allowing the HMF to vary. This provides a way of testing the validity of the halo model-HMF calibration using data. We find that the {\it Planck} cosmology is not compatible with the vanilla HMF for both the DES-y3 and the KiDS-1000 data. When the cosmology and the HMF parameters are allowed to vary, the {\it Planck} cosmology is no longer in tension. The modified HMF predicts a matter power spectrum with a $\sim 25\%$ power loss at $k\sim 1~{\rm h/Mpc}$, in agreement with the recent studies. We show that Stage IV surveys will be able to measure the HMF parameters with a few percent accuracy.Comment: 16 pages (including appendixes), 10 figures, 3 tables, main results in Figs. 5&

Minimising the impact of scale-dependent galaxy bias on the joint cosmological analysis of large scale structures

We present a mitigation strategy to reduce the impact of non-linear galaxy bias on the joint `$3 \times 2$pt' cosmological analysis of weak lensing and galaxy surveys. The $\Psi$-statistics that we adopt are based on Complete Orthogonal Sets of E/B Integrals (COSEBIs). As such they are designed to minimise the contributions to the observable from the smallest physical scales where models are highly uncertain. We demonstrate that $\Psi$-statistics carry the same constraining power as the standard two-point galaxy clustering and galaxy-galaxy lensing statistics, but are significantly less sensitive to scale-dependent galaxy bias. Using two galaxy bias models, motivated by halo-model fits to data and simulations, we quantify the error in a standard $3 \times 2$pt analysis where constant galaxy bias is assumed. Even when adopting conservative angular scale cuts, that degrade the overall cosmological parameter constraints, we find of order $1 \sigma$ biases for Stage III surveys on the cosmological parameter $S_8 = \sigma_8(\Omega_{\rm m}/0.3)^{\alpha}$. This arises from a leakage of the smallest physical scales to all angular scales in the standard two-point correlation functions. In contrast, when analysing $\Psi$-statistics under the same approximation of constant galaxy bias, we show that the bias on the recovered value for $S_8$ can be decreased by a factor of $\sim 2$, with less conservative scale cuts. Given the challenges in determining accurate galaxy bias models in the highly non-linear regime, we argue that $3 \times 2$pt analyses should move towards new statistics that are less sensitive to the smallest physical scales.Comment: 14 pages, 13 figures, accepted to be published in MNRA

Magnification bias in galaxy surveys with complex sample selection functions

Gravitational lensing magnification modifies the observed spatial distribution of galaxies and can severely bias cosmological probes of large-scale structure if not accurately modelled. Standard approaches to modelling this magnification bias may not be applicable in practice as many galaxy samples have complex, often implicit, selection functions. We propose and test a procedure to quantify the magnification bias induced in clustering and galaxy-galaxy lensing (GGL) signals in galaxy samples subject to a selection function beyond a simple flux limit. The method employs realistic mock data to calibrate an effective luminosity function slope, $\alpha_{\rm{obs}}$, from observed galaxy counts, which can then be used with the standard formalism. We demonstrate this method for two galaxy samples derived from the Baryon Oscillation Spectroscopic Survey (BOSS) in the redshift ranges $0.2 < z \leq 0.5$ and $0.5 < z \leq 0.75$, complemented by mock data built from the MICE2 simulation. We obtain $\alpha_{\rm{obs}} = 1.93 \pm 0.05$ and $\alpha_{\rm{obs}} = 2.62 \pm 0.28$ for the two BOSS samples. For BOSS-like lenses, we forecast a contribution of the magnification bias to the GGL signal between the angular scales of $100$ and $4600$ with a cumulative signal-to-noise ratio between $0.1$ and $1.1$ for sources from the Kilo-Degree Survey (KiDS), between $0.4$ and $2.0$ for sources from the Hyper Suprime-Cam survey (HSC), and between $0.3$ and $2.8$ for ESA Euclid-like source samples. These contributions are significant enough to require explicit modelling in future analyses of these and similar surveys.Comment: 15 pages, 13 figure

The effects of varying depth in cosmic shear surveys

We present a semi-analytic model for the shear two-point correlation function of a cosmic shear survey with non-uniform depth. Ground-based surveys are subject to depth variations that primarily arise through varying atmospheric conditions. For a survey like the Kilo-Degree Survey (KiDS), we find that the measured depth variation increases the amplitude of the observed shear correlation function at the level of a few percent out to degree-scales, relative to the assumed uniform-depth case. The impact on the inferred cosmological parameters is shown to be insignificant for a KiDS-like survey. For next-generation cosmic shear experiments, however, we conclude that variable depth should be accounted for

Pure-mode correlation functions for cosmic shear and application to KiDS-1000

One probe for systematic effects in gravitational lensing surveys is the presence of so-called B modes in the cosmic shear two-point correlation functions, ξ ± (ϑ), since lensing is expected to produce only E-mode shear. Furthermore, there exist ambiguous modes that cannot uniquely be assigned to either E-or B-mode shear. In this paper we derive explicit equations for the pure-mode shear correlation functions, ξ E/B ± (ϑ), and their ambiguous components, ξ amb ± (ϑ), that can be derived from the measured ξ ± (ϑ) on a finite angular interval, ϑ min ≤ ϑ ≤ ϑ max , such that ξ ± (ϑ) can be decomposed uniquely into pure-mode functions as ξ + = ξ E + + ξ B + + ξ amb + and ξ − = ξ E − − ξ B − + ξ amb −. The derivation is obtained by defining a new set of Complete Orthogonal Sets of E and B mode-separating Integrals (COSEBIs), for which explicit relations are obtained and which yields a smaller covariance between COSEBI modes. We derive the relation between ξ E/B/amb ± and the underlying E-and B-mode power spectra. The pure-mode correlation functions can provide a diagnostic of systematics in configuration space. We then apply our results to Scinet LIght Cone Simulations (SLICS) and the Kilo-Degree Survey (KiDS-1000) cosmic shear data, calculate the new COSEBIs and the pure-mode correlation functions, as well as the corresponding covariances, and show that the new statistics fit equally well to the best fitting cosmological model as the previous KiDS-1000 analysis and recover the same level of (insignificant) B modes. We also consider in some detail the ambiguous modes at the first-and second-order level, finding some surprising results. For example, the shear field of a point mass, when cut along a line through the center, cannot be ascribed uniquely to an E-mode shear and is thus ambiguous; additionally, the shear correlation functions resulting from a random ensemble of point masses, when measured over a finite angular range, correspond to an ambiguous mode