Extracting cosmological information from small scales in weak gravitational lensing data José Manuel Zorrilla Matilla Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2020 © 2020 José Manuel Zorrilla Matilla All Rights Reserved Abstract Extracting cosmological information from small scales in weak gravitational lensing data José Manuel Zorrilla Matilla This work is concerned with how to extract information encoded in small scales of non-Gaussian fields, with the purpose of learning about cosmology using weak gravitational lensing. We do so by comparing different methods on simulated data sets. The topic is relevant, for upcoming galaxy surveys will map the late evolution of the matter density field, which is non-Gaussian, with an unprecedented level of detail, and any improvement on the analysis techniques will increase the experiments’ scientific return. First, we investigate some non-Gaussian observables used in the weak lensing community. We analyze to what extent they are sensitive to the background expansion of the universe, and to what extent to the evolution of the structures responsible for the lensing. We then focus our attention on one such statistic, lensing peaks, and assess the performance of a simple halo-based model that has been proposed to forecast their abundance. We find some shortcomings of that semi-analytic approach, and proceed to review some minimal requirements for numerical simulations used to forecast non-Gaussian statistics, to reduce their computational cost while fulfilling the accuracy and precision required by future experiments. Second, we propose a novel measurement, that of the temperature dipole induced on the cosmic microwave background induced by the rotation of ionized gas around galaxies, as an additional observation to help constrain the distribution of baryonic matter on the smallest scales probed by WL experiments. The uncertainty in this distribution is a major theoretical systematic for future surveys. Third, we show how deep neural networks can be used to map pixel-level data into the cosmological parameters of interest, by-passing the previous compression step of measuring pre-designed statistics. We provide the first (simulation-based) credible contours based on neural networks applied to weak lensing data, and discuss how to interpret these models. Table of Contents List of Tables .......................................... vi List of Figures .......................................... x Acknowledgments ........................................ xxii Dedication ............................................xxiii Chapter 1: Introduction .................................... 1 1.1 Weak lensing cosmology ............................... 1 1.1.1 Weak lensing fundamentals.......................... 2 1.1.2 Experimental results ............................. 4 1.2 Cosmological inference based on WL measurements ................ 5 1.2.1 WL statistics ................................. 7 1.3 Deep learning applied to weak lensing cosmology.................. 9 1.3.1 Deep learning basics ............................. 10 1.3.2 Applications of deep learning to WL..................... 17 1.4 Structure of dissertation................................ 18 Chapter 2: Geometry and growth contributions to cosmic shear observables ......... 21 2.1 Introduction...................................... 21 i 2.2 Disentangling geometry from growth in simulations................. 23 2.2.1 Simulating weak lensing maps........................ 23 2.2.2 Isolating the effect of geometry vs. growth.................. 26 2.3 Sensitivity to Ω< and w ................................ 27 2.3.1 Power spectrum................................ 28 2.3.2 Equilateral bispectrum ............................ 30 2.3.3 Lensing peaks................................. 32 2.3.4 Minkowski functionals............................ 34 2.4 Impact on parameter inference ............................ 36 2.5 Discussion....................................... 41 2.6 Conclusions...................................... 44 Chapter 3: Do dark matter halos explain lensing peaks? ................... 48 3.1 Introduction...................................... 48 3.2 Predicting peak counts ................................ 50 3.2.1 N-body simulations.............................. 51 3.2.2 Camelus.................................... 52 3.2.3 Parameter inference.............................. 52 3.3 Results......................................... 57 3.4 Discussion....................................... 66 3.5 Conclusions...................................... 75 Chapter 4: Optimizing simulation parameters for weak lensing analyses involving non- Gaussian observables ............................... 77 ii 4.1 Introduction...................................... 77 4.2 Methods........................................ 78 4.2.1 Simulating convergence maps ........................ 78 4.2.2 Assessing the impact of hyper-parameters.................. 81 4.2.3 Hyper-parameter configurations ....................... 83 4.2.4 Observables.................................. 84 4.3 Results and discussion ................................ 89 4.3.1 Lens plane thickness ............................. 89 4.3.2 Mass resolution................................ 96 4.4 Conclusions......................................101 Chapter 5: Probing gaseous galactic halos through the rotational kSZ effect ......... 105 5.1 Introduction......................................105 5.2 Modeling the rotational kSZ (rkSZ) signal from galaxies . 106 5.2.1 The rkSZ imprint on the CMB........................106 5.2.2 Galactic atmospheres: electron density....................107 5.2.3 Galactic atmosphere: kinematics.......................110 5.3 Characterizing the observed rkSZ signal.......................112 5.3.1 Aperture filter.................................114 5.3.2 Matched filter.................................115 5.4 Measurement signal-to-noise and required number of galaxies . 115 5.5 Stacking Planck data at the positions of MaNGA galaxies . 122 5.5.1 Galaxy data: MaNGA.............................122 iii 5.5.2 CMB data: Planck ..............................124 5.5.3 Stacking....................................124 5.6 Discussion.......................................129 5.6.1 Model and observational uncertainties....................129 5.6.2 Measurement uncertainties..........................132 5.6.3 Detection feasibility..............................133 5.7 Conclusions......................................136 Chapter 6: Non-Gaussian information from weak lensing data via deep learning ...... 139 6.1 Introduction......................................139 6.2 Data..........................................142 6.2.1 Mock convergence maps ...........................142 6.2.2 Neural network training and architecture...................144 6.2.3 Alternative descriptors ............................149 6.3 Results.........................................152 6.4 Discussion.......................................157 6.4.1 Non-Gaussian information extracted by the neural network . 157 6.4.2 Effect of the smoothing scale on the results . 160 6.4.3 Bias in the CNN predictions .........................163 6.5 Conclusions......................................165 Chapter 7: Interpreting deep learning models for weak lensing ................ 167 7.1 Introduction......................................167 7.2 Model and data ....................................169 iv 7.3 Network performance relative to alternative statistics . 170 7.4 Interpreting DNNs with saliency methods ......................175 7.4.1 Method comparison and selection ......................177 7.4.2 Mapping attributions back to physical space . 180 7.5 Discussion and conclusions..............................182 Chapter 8: Conclusions and future work ........................... 184 8.1 Summary of results..................................184 8.2 Future work......................................186 References ............................................ 212 Appendix A: Gaussian likelihood approximation ....................... 213 Appendix B: Sensitivity of results to interpolation ...................... 216 Appendix C: Impact of filter misalignment and centering errors. ............... 218 Appendix D: Variance of aperture filter dipole measurements ................ 221 Appendix E: Selecting galaxies from MaNGA for stacking. ................. 223 v List of Tables 2.1 Parameters of the eight models explored around the fiducial model (Ω< = 0.26, F = −1.0). All models are spatially flat with ΩΛ = 1 − Ω< and consider a constant equation of state parameter F for DE. ........................ 23 2.2 Δ j2 for different cosmological models computed for the power spectrum and three non-Gaussian observables (equilateral bispectrum, peak counts and Minkowski functionals) over noisy ^ maps with source galaxies at either I = 1 or I = 2. 37 2.3 Marginalized errors on Ω< and F, orientation of the Fisher ellipse (measured as the angle between its major axis and the F axis), and figure-of-merit (FOM; defined as c/, with the area of the error ellipse). The errors correspond to a 68% confidence level, scaled to a 1000 deg2 survey. All calculations were done on noisy ^ maps with source galaxies at either I = 1 or I = 2. 39 3.1 Cosmological parameters for the fiducial model. All other cosmologies share these parameters except Ω< and f8. ............................ 50