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The next generation of galaxy surveys is ushering in a new era of precision cosmology. This progress opens unprecedented opportunities to probe physics beyond the standard cosmological model, even in scenarios where the dark sector remains completely secluded from the visible sector. In this talk, I will present several examples of novel dynamics that leave distinct imprints on both linear and non-linear cosmological observables, including long-range forces within the dark sector and cosmological phase transitions. I will also emphasize the importance of developing new observables to further characterize the underlying dynamics of the dark sector.