How close can an inhomogeneous universe mimic the concordance model?

Recently, spatially inhomogeneous cosmological models have been proposed as an alternative to the Lambda CDM model, with the aim of reproducing the late time dynamics of the Universe without introducing a cosmological constant or dark energy. This paper investigates the possibility of distinguishing such models from the standard Lambda CDM using background or large scale structure data. It also illustrates and emphasizes the necessity of testing the Copernican principle in order to confront the tests of general relativity with the large scale structure.