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Abstract

With the arrival of next-generation cosmological observations, this thesis develops a general framework to probe gravity across a wide range of cosmological scales. It constructs robust, model-independent observables that quantify deviations from the standard scenario and evaluates how well future surveys can constrain them, with the goal of challenging the very foundations of our understanding of the Universe. Assuming that dark matter and baryons follow the same geodesics, we construct estimators of modified gravity using galaxy clustering and weak lensing observations. Two quantities, the effective gravitational coupling μG and the gravitational slip parameter η, are expressed in terms of model-independent observables. Forecasts for a combined DESI- and Euclid-like survey show that these parameters can be constrained to the 10–30% level within this fully agnostic framework. We then incorporate potential violations of the weak equivalence principle. These effects are encoded as modifications to the Euler equation. We find that an observable EP , which encapsulates equivalence principle violation, can be constructed from relativistic corrections in the cross-correlation of two galaxy populations and measured with future SKA surveys. Moreover, by combining galaxy number counts with supernova luminosity distance fluctuations, we show that this allows for a direct reconstruction of η, even when the Euler equation is modified. The analysis is further extended to include dark matter viscosity, which can mimic both modified gravity and equivalence principle violations. We find that the present-day viscosity parameter can be constrained to the O(10−7) level. In addition, we investigate nonlinear structure formation in scale-dependent modified gravity, focusing on Horndeski theories. Using the Wronskian method, we derive analytic expressions for the second- and third-order standard perturbation theory kernels, which are relevant for computing the one-loop galaxy power spectrum. Scale-dependent bias and redshift-space distortion corrections are also included. This thesis establishes a robust, data-driven framework for testing gravity, using probes from relativistic effects on the largest cosmological scales to nonlinearities on smaller scales. The methods developed here are directly applicable to future surveys and offer a powerful path toward model-independent constraints on fundamental physics.