Model-independent test of modified gravity

The theory of gravity holds significant importance in our understanding of the large-scale structure and dynamics of the Universe. We first demonstrate how one can measure the gravitational slip, η, in a model-independent way by combining observations from galaxy clustering and weak lensing. Additionally, we propose a method to test the cosmological Poisson equation model-independently while maintaining independence from specific models for the background expansion, the power spectrum shape, and the non-linear corrections. We show that one can only measure the combination M≡Ω_{m,0}μ, where μ quantifies the deviation of the Poisson equation from the standard one and Ω_{m,0} is the present matter density fraction. We also obtain constraints on M for a survey that approximates a combination of the Dark Energy Spectroscopic Instrument and Euclid by employing a recent model-independent forecast for the growth rate f(z) and the expansion rate E(z).