With the upcoming generation of galaxy surveys such as Euclid, LSST (Vera Rubin Observatory) DESI and SKAO, among others, the cosmological community will have groundbreaking measurements of the Large Scale Structure of the Universe. These measurements will provide very precise information about the expansion rate, the growth of non-linear structures as a function of scale and the impact of baryonic feedback. These measurements have to be confronted against theoretical models that aim to explain the nature of Dark Matter, Dark Energy and possibly resolve the ongoing tensions we face in cosmology, such as the H0 and the S8 discrepancies. In this talk I will recall some of the competing and alternative models to the standard LCDM paradigm that have been proposed in the literature in the last decades, focusing on scalar-tensor theories with and without screening and generalized parametrizations of Modified Gravity. I will discuss how, with the combined observations from Euclid (especially with the complementarity of Weak Lensing and Galaxy Clustering) and the advent of Radio-cosmology, we expect to be able to constrain that vast theoretical parameter space. By doing so, we will also hopefully measure the neutrino mass and learn about the fundamental physics of baryons and non-linear structure formation. Towards the end I will discuss also the challenges we face in computational complexity and how this is being resolved with emulators and the emerging field of differentiable programming.
What will Large Scale Structure tell us about Dark Energy in the next decade?