Towards a model independent approach to galaxy clustering

The next decade will represent a scientific golden age for cosmology, since forthcoming generation of galaxy surveys will sample the large scale structure of the universe over large volumes, making it possible to test cosmological models with unprecedent precision. LCDM, with an early epoch driven by inflation, is the standard paradigm for the origin and the evolution of the universe. The cosmological observations of the last decades have driven us to understand the composition of our universe at a very deep level, but still some intriguing questions and issues remain to be faced. Modified gravity (MG) theories, primordial non-gaussianities (PNG) and neutrino masses are only few examples of possible deviations from the standard model which can affect the non-linear process of galaxy clustering. In this thesis I will present how to study galaxy clustering in a model independent way using only symmetry principles, like the equivalence principle and the (extended) Galilean invariance. I will introduce the consistency relations of large scale structure and I will show how to use them to constraint cosmological parameters. I will also present a new approach to construct cosmological correlators in a systematic and perturbative way via the large scale structure Bootstrap.