Robust Estimation Techniques for the Cosmological Analysis of Large Scale Structure
The ΛCDM model of cosmology together with Inflation has had tremendous success over the past 30 years in explaining the increasingly rich data sets of the cosmic microwave background and large-scale structure. The next generation of large-scale structure surveys is expected to answer many open questions about the microscopic description of the Universe. In order to fully leverage those data sets, one needs exquisite theoretical predictions. Here, the main difficulty is the non-linear nature of the large-scale structure observables which, together with the exquisitely small statistical errors, cause real concern of false discoveries. In this thesis, we study two estimators that allow us to extract non-linear information from the large-scale structure while being robust against one of the leading sources of systematic uncertainties: Redshift-space distortions. By means of a bias relation, we extend the matter counts-in-cells statistic for the first time to neutral hydrogen. Neutral hydrogen is particularly interesting for counts-in-cells statistics because of the vast regions that can be covered by intensity mapping. We find percent-level accuracy when comparing the prediction for the density in spheres probability density function to the IllustrisTNG simulation. The measured density dependent clustering signal, which could be used to break the bias-amplitude degeneracies, matches theoretical expectations. Our bias model is able to capture the effect of redshift-space distortions making the estimator robust. Based on a separation idea, we present an efficient code to compute projected bispectra. The separation approach is orders of magnitude more efficient than the direct integration. This allows us to investigate the relation between biases in the estimated parameters and inaccurate modelling of non-linear redshift-space distortions for the power spectrum and bispectrum of projected galaxy density fields and lensing convergence. For a toy galaxy survey that resembles the CMASS sample of the baryon oscillation spectroscopic survey, we find that modelling non-linear redshift-space distortion only becomes necessary for galaxy bins thinner than 150 Mpc/h. In case a better radial resolution is available, errors on cosmological parameters can be improved by 20% when including an accurate non-linear RSD model that allows us to use bins of depth ∼60 Mpc/h. The separation of projection integrals proves also useful for theoretical uncertainties. We use the separability of Gaussian correlation functions to develop a consistent model for theoretical uncertainties of the projected power spectrum.
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