The Copernican Principle states that the Earth holds no special place in the universe and that our observation of the universe is similar to that seen from any other position.
One of our research groups recently published a paper in the Journal of Cosmology and Astroparticle Physics, below is an abstract by Sean February of UCT's Department of Mathematics and Applied Mathematics:
In this work, we simulated the distribution of galaxies that would arise in a non-standard cosmological model of the universe, and compared it to the standard one. The standard model fits the observations well, but unfortunately requires the existence of an unknown force that drives the inferred accelerated expansion. The alternative 'void' model we studied has generally fared well in describing the observations without this 'dark energy', however it requires us to occupy a special place in the cosmos i.e. near the center of the observable universe. Note, however, that the uniqueness of our location remains to be observationally verified. The main calculation involves a complicated double integral, and the ICTS HPC clusters have proved perfect for the job, as we were able to perform higher accuracy runs in a reasonable amount of time. Our results revealed an important test to distinguish such void models from the standard model.