Dark-energy dependent test of general relativity at cosmological scales

5 pages, 3 figures. Accepted for publication in Physical Review DInternational audienceThe Lambda CDM framework offers a remarkably good description of our universe with a very small number of free parameters, which can be determined with high accuracy from currently available data. However, this does not mean that the associated physical quantities, such as the curvature of the universe, have been directly measured. Similarly, general relativity is assumed, but not tested. Testing the relevance of general relativity for cosmology at the background level includes a verification of the relation between its energy contents and the curvature of space. Using an extended Newtonian formulation, we propose an approach where this relation can be tested. Using the recent measurements on cosmic microwave background, baryonic acoustic oscillations and the supernova Hubble diagram, we show that the prediction of general relativity is well verified in the framework of standard $\Lambda$CDM assumptions, i.e. an energy content only composed of matter and dark energy, in the form of a cosmological constant or equivalently a vacuum contribution. However, the actual equation of state of dark fluids cannot be directly obtained from cosmological observations. We found that relaxing the equation of state of dark energy opens a large region of possibilities, revealing a new type of degeneracy between the curvature and the total energy content of the universe