>Magister Scientiae - MSc / Next-generation surveys of the large-scale structure of the Universe will be of great importance in allowing us to extract invaluable information about the nature of the Universe and the physical laws that govern it, at a higher precision than previously possible. In particular, they will allow us to more closely study primordial non-Gaussianity, a feature which leaves an imprint on the power spectrum of galaxies on the ultra-large scales and which acts as a powerful probe of the physics of the early Universe. To investigate the extent to which upcoming surveys will be able to improve our knowledge of primordial non-Gaussianity, we perform a forecast to predict the observational constraints on local-type primordial non-Gaussianity, as well as an extension that includes a scale dependence. We study the constraining power of a multi-tracer approach, where information from different surveys is combined to help suppress cosmic variance and break parameter degeneracies. More specifically, we consider the combination of a 21cm intensity mapping survey with each of two different photometric galaxy surveys, and also examine the effect of including CMB lensing as an additional probe. The forecast constraint from a combination of SKA1, a Euclid-like (LSST-like) survey and a CMB Stage 4 lensing experiment is (fNL) ' 0:9 (1:4) which displays a factor of 2 improvement over the case without CMB lensing, indicating that the surveys considered are indeed complementary. The constraints on the running index of the scale-dependent model are forecast as (nNL) ' 0:12 (0:22) from the same combination of surveys.

Galaxy redshift surveys are powerful probes of cosmology. Yet, in order to fully exploit the information contained in galaxy surveys, we need to improve upon our understanding of the structure formation in the Universe. Galaxies are formed/observed at late times when the density field is no longer linear so that understanding non-linearities is essential. In this thesis, we show that, at high redshifts, we can accurately model the galaxy power spectrum in redshift space by using the standard cosmological perturbation theory. Going beyond the power spectrum, we can use the three-point function, or the bispectrum, to gain important information on the early universe as well as on the galaxy formation via measurements of primordial non-Gaussianity and galaxy bias. We show that the galaxy bispectrum is more sensitive to primordial non-Gaussianities than previously recognized, making high-redshift galaxy surveys a particularly potent probe of the physics of inflation. Weak lensing offers yet another way of probing cosmology. By cross correlating the angular position of galaxies with the shear measurement from galaxy lensing or CMB lensing, we also show that one can obtain the information on cosmological distance scale, the galaxy bias, and the primordial non Gaussianity from weak lensing method. / text