Science is all about models of reality. Nature is way too complicated to be studied in every single detail and science begins when we find clever ways to simplify reality, that is, to get rid of uninteresting facts to focus on the important ones. The lessons we learn from this simplified view can then be applied to other problems, in the hope to find general form of description, that we call theories. Once a theory is established, that is, it works well explaining the experimental results, we enrich and complete it by taking into account more and more phenomena.
In doing this, of course, the difficulty consists in find “clever ways to simplify reality”. If we simplify it too much, for instance assuming that because our own Galaxy is relatively stable then the entire Universe must be, we would not discover the cosmic expansion, as Einstein learned the hard way. If we don’t simplify it enough, on the other hand, we risk doing “Babylonian science”, an endless collection of phenomena without any theoretical understanding (a disclaimer: modern archaeologists however warn against assuming that what we find in surviving Assyrian cuneiform tablets represents all of that ancient culture; maybe they also had their own Aristotle, Newton, and Einstein, but no trace remained).
Similarly, in cosmology we try to obtain results that are as independent as possible of assumptions, but of course we cannot avoid making at least some kind of them. In a recent paper (see also this review) we tried to isolate and measure a combination of observable cosmological quantities that can assess whether gravity is Einsteinian or not, without first assuming that, for instance, our Universe is based on the standard LambdaCDM cosmological model, or that the functions that describe the growth of structure are independent of space or time. We find indeed that by combining gravitational lensing, galaxy clustering, and the so-called redshift distortions, one can achieve a somewhat model-independent measure of a parameter, called eta, that measures whether the two gravitational potentials that define gravity in general relativity are equal or not. If they are equal, then Einstein’s theory is correct also at cosmological scales. In the other case, some new force acting on top of gravity must be present in our Universe.
We applied our formalism for the first time to all existing cosmological data. The result is not particularly impressive: we find that Einstein’s gravity is fine, but the data uncertainty is so large that almost all models of modified gravity are also still alive. However, we are now confident that our method works well and can deliver the promise of a relatively model-independent test of gravity. So we wait impatiently for new and better data, for instance from the Euclid satellite, and see if our models of reality can become a bit more real.