Gravity is curved geometry: A fact of nature or model-dependent interpretation? We are regularly taught in high-schools and universities that, according to General Relativity (GR), gravity is nothing but a manifestation of space-time curvature (which, in its turn, is caused by matter and energy). However, GR is still only a model, which hasn't been challenged by experimental evidence/precision thus far. E.g., in wiki one might find a lot of alternatives to GR, some of which agree with observations not worse than GR (e.g., Brans-Dicke theory). There are theories which describe gravity not in terms of curvature, but in terms of torsion - but in reality gravity cannot be both at the same time! Besides, as far as I understand, curved space might be described as a curved surface in non-curved space of a higher dimension.
So my question is: do I miss something and there are strong model-independent reasons to believe that gravity is geometry, or is it just that authors in most textbooks and articles imply that this is a model-dependent interpretation, without saying it explicitly?
 A: The interpretation of gravity as curvature of spacetime is model-dependent. You already mentioned the teleparallel equivalent of general relativity, modelling gravity by torsion. Another possibility are bi-metric theories, where the metric is a more ordinary field on a fixed background (this should be more in line with how string theorists tend to think of gravity - it's just another field, but somewhat special because it has spin 2).
However, GR does have a few things going for it: For example, in principle, we could violate the equivalence principle in teleparallel gravity. So if we're going that way, the equivalence principle becomes a new assumption, whereas in GR, it follows naturally from the geometry. Similarly, if a bi-metric theory is equivalent to GR, the background metric needs to be un-observable, and that's something of a 'design-smell'.
GR is the most aesthetically pleasing description of gravity I'm aware of - which has no relevancy to how the universe 'really' works. That's not a question physics can answer - science is not in the business of 'everlasting truth'.
