Towards Robust Quantification of Cosmological Errors

The method of baryon acoustic oscillation (BAO) is among the best probes of the dark energy equation of state, and worldwide efforts are being invested in order to perform measurements that are accurate at the percent level. In current data analyses, however, estimates of the error about the BAO are based on the assumption that the density field can be treated as Gaussian, an assumption that becomes less accurate as smaller scales are included in the measurement. It was recently shown from large samples of N-body simulations that the error bars about the BAO obtained this way are in fact up to 15-20 per cent too small. This important bias has shaken the confidence in the way error bars are calculated, and is motivating developments of analyses pipelines that include non-Gaussian features in the matter density fields. In this thesis, we propose general strategies to incorporate non-Gaussian effects in the context of a survey. After describing the high performance N-body code that we used, we present novel properties of the non-Gaussian uncertainty about the matter power spectrum, and explain how these combine with a general survey selection function. Assuming that the non-Gaussian features that are observed in the simulations correspond to those of Nature, this approach is the first unbiased measurement of the error bar about the power spectrum, which simultaneously removes the undesired bias on the BAO error. We then relax this assumption about the similitude of the non-Gaussian natures in simulations and data, and develop tools that aim at measuring the non-Gaussian error bars exclusively from the data. It is possible to improve the constraining power of non-Gaussian analyses with `Gaussianizations' techniques, which map the observed fields into something more Gaussian. We show that two of such techniques maximally recover degrees of freedom that were lost in the gravitational collapse. Finally, from a large sample of high resolution N-body realizations, we construct a series of weak gravitational lensing distortion maps and provide high resolution halo catalogues that are used by the CFTHLenS community to calibrate their estimators and study many secondary effects with unprecedented accuracy.Ph