Falsifying LCDM: model-independent tests of the concordance model of cosmology

The concordance LCDM model has been very successful at reproducing a wide range of observations. However, the nature of its main components, such as dark energy, dark matter, and inflation, are still unkown. Therefore, it is of prime importance to question the underlying hypotheses of the model and tests there prediction. While most constraints have been obtained assuming a LCDM universe, model-independent approaches, which do not make assumptions regarding the model, are a powerful approach. To falsify the LCDM model, I applied model-indepedent methods to the latests available data to test different aspects of the concordance model, such as the FLRW metric, the curvature, dark energy as the cosmological constant, and gravity as general relativity. The Universe is consistent with flat-LCDM with GR. However, at z>1, tensions start to appear, and more data are required.