PRECISE AND ACCURATE MEASUREMENTS OF COSMOLOGICAL PARAMETERS FROM GALAXY CLUSTERING AND MOTIONS

Measurements of the growth rate of large scale structure in the Universe are crucial to pinpoint the origin of cosmic acceleration, distinguishing whether it requires the existence of "dark energy", or rather a modification of General Relativity. Galaxy clustering measured in redshift space contains the imprint of such growth in the form of a measurable large-scale anisotropy. These redshift-space distortions (RSD) are produced by the coherent peculiar velocity flows towards overdensities, which add to the cosmological redshift. The present Thesis is focused on improving our ability to extract measurements of the growth rate from galaxy redshift surveys. To this end, I have first tested the performances of standard estimators, using numerical simulations. I find that the traditional dispersion model is affected by a systematic error larger than the statistical ones expected from current/future galaxy surveys. To improve on this, I have then developed a novel description of the line-of-sight pairwise velocity distribution, which is a crucial ingredient in modelling RSD. Using a principal component analysis, I find that redshift-space clustering on all scales can be described by a minimum set of four eigenfunctions of the velocity distributions. Inspired by these findings, I have then proposed an alternative parametrization in which the link to the underlying physics is more explicit. This is obtained by describing the overall velocity distribution as a superposition of local Gaussian velocity distributions, whose mean and standard deviation are, in turn, distributed according to a bivariate Gaussian. Tests of this model against simulations show that it is general enough to correctly describe RSD on all scales, capturing surprisingly well the dynamics of the galaxy flow. This opens a new horizon for the development of a complete model of redshift-space distortions based on the formally exact "streaming model" approach.