Fundamental physics tests with the large-scale structure of the Universe

The current LCDM cosmological model offers a phenomenological description of the Universe, in terms of relatively few ingredients. However, its theoretical foundations still remain elusive. This thesis explores how the large-scale structure of the Universe can offer novel insights into open issues, such as the nature of dark matter, the early Universe and the initial conditions of structure formation, imprints of new physics beyond the Standard Model of particle physics. The strategy to search for signatures of new physics is twofold. On the one hand, new observables and new combinations of existing probes are needed; on the other hand, a more accurate theoretical modeling of the observables is needed, in order to match the precision and accuracy of future observations. The first part of the thesis will focus on the clustering pattern of galaxies - in particular on the antisymmetric galaxy cross-correlations and on imprints of fossil fields in the large-scale structure. The second part will investigate the potentialities of 21-cm line-intensity mapping at high redshifts, in the epoch that precedes the formation of the first stars. Finally, an example will be given of how the stochastic gravitational wave background can provide information on fundamental physics. In all these cases, the theoretical modeling will be developed, followed by a forecast study for future surveys.