Model independent tests of LCDM

The standard cosmological model (LCDM) has shown a great ability to explain cosmological observations throughout the past 3 decades. Despite this, several of its component are still a mystery from the theoretical point of view; together with the observational tensions recently found between different measurements of its parameters, this motivates the search for alternative models or, at least, a thorough testing of LCDM. In this talk, I will focus mostly on tests of one of the crucial assumptions done in cosmology, i.e. that General Relativity is a good description of gravity at cosmological scales, showing recent constraints and how upcoming surveys might improve our knowledge. In addition to this I will also show results on the consistency between different sectors of the LCDM model, as well as on other fundamental assumptions, such as the validity of the Distance Duality Relation. Finally, I will also briefly summarize how new cosmological observables might shed new light on the dark components of the standard cosmological model.