Constraining the Dark Sector with Galaxy Clustering

The nature of dark matter and the value of the neutrino masses remain among the central open questions in physics, and the clustering of galaxies has become one of the most promising probes for addressing them. The statistical power of current surveys, however, is outrunning our ability to fully exploit it. On the theory side, the galaxy power spectra analysis methods have been developed assuming a purely cold and non-interacting dark sector, so that the control of theoretical systematics is already a limiting factor. On the observational side, analyses restricted to the galaxy power spectrum alone are suboptimal, and ultimately limited by degeneracies that single statistics cannot break. This thesis addresses these limitations along three complementary directions. First, the redshift-space clustering of biased tracers in massive neutrino cosmologies is examined on N-body simulations, clarifying an ambiguity in the connection between halos and underlying matter. Second, a first step is taken towards extending the Effective Field Theory of Large-Scale Structure to cosmologies containing a non-cold dark matter subcomponent, including a self-consistent treatment of the coupled nonlinear evolution at one-loop level. Third, the projected bispectrum of the galaxy overdensity in combination with CMB lensing is validated and employed, for the first time, as a cosmological probe. The methods developed along these lines are then brought together in an original analysis of DESI DR1 full-shape measurements combined with Planck and ACT DR6, including lensing. This places the most stringent constraints to date on ultra-light axions as a subcomponent of dark matter, excluding, over a range of masses, subpercent fractions of the total matter density. Taken together, these studies pave the way for a more systematic and controlled exploration of the dark sector with the data of the coming decade.