Statistical and Numerical Methods for Precision Cosmology - Maion, Francisco Germano (2021)
The current cosmological model tells us that the Universe began very homogeneous, and matter slowly started clumping to make up stars, galaxies, clusters of galaxies, and the large scale structure that we see. The rate with which these structures were formed is very dependent on the theory that describes gravity. Measuring the multipoles of the power spectrum in redshift space we can probe this growth-rate, and thus constrain alternative models of gravity. In this work we review techniques to accurately measure the multipoles of the power spectrum, and to maximize the amount of information contained in these quantities. We also do a careful treatment of systematical effects, reviewing techniques to forward model these effects into the theoretical model for the power-spectrum multipoles. Combining these techniques, we were able to develop a pipeline capable of taking raw galaxy positions and turning them into unbiased cosmological parameters; furthermore, we have extensively tested it, and applied it to obtain constraints with data from the VIPERS survey. We have also done complementary work on understanding the noise in numerical simulations of the large scale structure. In particular, we have studied techniques to reduce the noise in statistics derived from numerical simulations, and were the first to give a detailed explanation of the process through which the fixing and pairing technique works to reduce the variance in n-point functions.