The Practical Use of Cosmic Shear As a Probe of Gravity
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The Practical use of Cosmic Shear as a Probe of Gravity Donnacha Kirk Thesis submitted for the Degree of Doctor of Philosophy of the University College London Department of Physics & Astronomy UNIVERSITY COLLEGE LONDON April 2011 I, Donnacha Kirk, conﬁrm that the work presented in this thesis is my own. Where information has been derived from other sources, I conﬁrm that this has been indicated in the thesis. Speciﬁcally: • The work on luminosity functions and red galaxy fractions in section 2.7 was done by Dr. Michael Schneider (then at Durham) as part of our collaboration on the paper Kirk et al. (2010). • The work in chapters 3 & 4 is my contribution to, and will form the substantial part of, papers in preparation with collaborators Prof. Rachel Bean and Istvan Lazslo at Cornell University. The MG effect on the linear growth function was computed by Istvan Lazslo. • The Great08 section of chapter 6 draws on my contributions to the Great08 Handbook (Bridle et al. 2009), Great08 Results Paper (Bridle et al. 2010a) and Great10 Handbook (Kitching et al. 2010). To Mum and Dad, for everything. Boyle. ... an’ it blowed, an’ blowed – blew is the right word, Joxer, but blowed is what the sailors use... Joxer. Aw, it’s a darlin’ word, a daarlin’ word. Boyle. An’, as it blowed an’ blowed, I often looked up at the sky an’ assed meself the question – what is the stars, what is the stars? Voice of Coal Vendor. Any blocks, coal-blocks; blocks, coal-blocks! Joxer. Ah, that’s the question, that’s the question – what is the stars? Boyle. An’ then, I’d have another look, an’ I’d ass meself – what is the moon? Joxer. Ah, that’s the question – what is the moon, what is the moon? — Juno and the Paycock Act I ABSTRACT This thesis deals with the practical application of Weak Gravitational Lensing (WGL) as a tool for studying two of the most challenging problems in modern cosmology: the nature of dark energy and tests of Einstein’s General Relativity. To be a useful tool, WGL must be able to put robust constraints on the parameters of interest even in the presence of a strong systematic effect like the Intrinsic Alignment (IA) of galaxies. In chapter 2 we demonstrate how ignoring the effect of IAs will lead to strongly biased mea- surements of cosmology. We introduce a simple IA model and demonstrate how the bias can be removed, at the cost of weaker constraints, by marginalising over nuisance parameters in the model. We present the ﬁrst joint constraints on IAs and cosmology from WGL and galaxy position information. The combination returns errorbars of the same order as the naive WGL calculation which ignored IAs. We extend the IA model to treat shear and position correlations in a uniﬁed way with > 100 nuisance parameters. We parameterise deviations from GR and show, in chapter 3, how the con- siderable (∼75%) decrease in constraining power caused by IAs can be partially mitigated by the inclusion of position-position and shear-position correlations. In chapter 4 we ﬁnd these results to extend across a wide range of survey speciﬁcations. We ﬁnd that increased survey area is not al- ways favoured at the expense of source density and that the impact of improved redshift knowledge is not dramatic. In chapters 5-7 we note the potentially very powerful constraints from a joint analysis of WGL and Redshift Space Distortions (RSDs) from a spectroscopic survey. We summarise some important preparatory work for future cosmic shear surveys and advances in shear measurement techniques before concluding and describing some directions for future work. v CONTENTS Abstract vi Table of Contents vii List of Figures xii List of Tables xiv 1 Introduction 1 1.1 Cosmology & the ΛCDM paradigm . 3 1.1.1 The Metric . 3 1.1.2 Expansion and Redshift . 5 1.1.3 Distances . 5 1.2 Gravity . 8 1.2.1 Relativity- Galileo, Newton, Einstein . 8 1.2.2 General Relativity . 9 1.2.3 Modiﬁed Gravity Theories . 10 1.3 Dynamics, Perturbations & Structure growth . 10 1.3.1 Perturbations and Growth of Structure . 12 1.4 The Early Universe . 13 1.4.1 The Big Bang . 13 1.4.2 Inﬂation . 14 1.4.3 The Post-Inﬂation Universe . 16 1.5 Energy Components of the Universe . 17 1.5.1 Baryonic Matter . 17 vi Contents vii 1.5.2 Dark Matter . 18 1.5.3 Dark Energy . 20 1.5.4 Neutrinos . 22 1.5.5 Radiation & Curvature . 23 1.6 Cosmic Probes . 23 1.6.1 LSS . 23 1.6.2 CMB . 26 1.6.3 Supernovae . 28 1.7 Weak Gravitational Lensing . 30 1.7.1 Gravitational Lensing . 30 1.7.2 Weak Gravitational Lensing . 35 1.7.3 Cosmic Shear . 36 1.7.4 Shear Measurement . 41 1.7.5 WGL Systematics . 44 1.7.6 Cosmic Shear Surveys . 45 1.7.7 Beyond Cosmic Shear . 46 1.7.8 Beyond the Optical . 48 1.8 Thesis Structure . 49 2 Simultaneous constraints on intrinsic alignments and cosmology from current data 50 2.1 Introduction . 50 2.2 Cosmic Shear and intrinsic alignments . 53 2.2.1 Cosmic Shear . 54 2.2.2 Intrinsic Alignments . 54 2.3 Shear-shear correlations . 60 2.3.1 Cosmic Shear Data . 60 2.3.2 Correlation Functions Including Intrinsic Alignments . 62 2.3.3 Impact on σ8 constraints . 64 2.3.4 Impact on constraints on σ8 and Ωm .................... 65 2.4 Shear-position correlations . 67 2.4.1 Data . 67 2.4.2 Correlation Functions . 67 2.4.3 Constraints on Intrinsic Alignment Parameters . 69 Contents viii 2.5 Joint shear-shear and shear-position constraints . 70 2.5.1 Joint Constraints on Intrinsic Alignment Parameters . 71 2.5.2 Joint Constraints on Cosmology . 73 2.6 Conclusions . 76 2.7 Appendix- Models for mean luminosity and red galaxy fraction . 80 3 The Effect of Intrinsic Alignments on Constraining Modiﬁed Gravity with Cosmic Shear 84 3.1 Introduction . 84 3.2 Formalism . 86 3.2.1 Observables . 86 3.2.2 Intrinsic Alignments . 89 3.2.3 Modiﬁed Gravity . 91 3.2.4 Comprehensive Bias Model . 93 3.3 Likelihood analysis . 95 3.3.1 Survey speciﬁcations . 95 3.3.2 Characterizing the likelihood surface . 98 3.4 Analysis . 98 3.5 Conclusions . 104 4 Measuring Modiﬁed Gravity with Future Cosmic Shear Surveys including Intrinsic Alignments 107 4.1 Introduction . 107 4.2 Cosmological Set-Up . 110 4.2.1 General Cosmology . 110 4.2.2 Cosmic Shear . 111 4.2.3 Intrinsic Alignments . 111 4.2.4 Galaxy Position Data . 112 4.2.5 Modiﬁed Gravity . 113 4.2.6 Summary of Chapter 3 results . 114 4.2.7 General Survey Parameters . 114 4.3 Survey area . 116 4.4 Photometric Redshifts . 121 4.4.1 Redshift Priors . 125 Contents ix 4.5 Spectroscopic redshifts . 129 4.6 Conclusions . 132 5 Combining Imaging and Spectroscopy: the case for DES & DESpec 134 5.1 Introduction . 134 5.1.1 DESpec . 136 5.2 The impact of redshift accuracy on WGL . 138 5.3 Redshift Space Distortions . 140 5.4 Modiﬁed Gravity and spec-z surveys . 144 5.5 Cross-correlations . 147 6 Image simulations for GREAT08 and DES 150 6.1 GREAT08 . 150 6.1.1 Introduction . 150 6.1.2 The Backward Process . 151 6.2 GREAT08 Concept . ..