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The debate in cosmology concerning LambdaCDM and MOND depends crucially on their respective ability of modelling across scales, and dealing with some of the specific problems that arise along the way. The main upshot of this article is to present three main problems facing multi-scale modelling in contemporary cosmology. The LambdaCDM model, which is the standard and by far most successful current cosmological model, faces what I call the downscaling problem when it comes to explain some recalcitrant evidence at the scale of individual galaxies, such as the mass-discrepancy acceleration relation (MDAR) and the baryonic Tully-Fisher relation (BTF). While the fastgrowing development of computer simulations has addressed these problems, nagging worries remain about some of the epistemic limits of these computer simulations in retrieving (as opposed to explaining) the data. The so-called upscaling problem affects MOND and its ability not just to explain but even simply retrieve large-scale structure and galaxy clusters. Recent attempts at extending MOND (EMOND) have had a limited empirical success, and are still far from providing a consistent explanation for possible formation mechanisms at the large-scale structure. Finally, the in between scales problem affects proposals designed to achieve the best of both worlds at the meso-scale. This is a fascinating area from a physical and a philosophical point of view, where the main challenge is the ability to have genuine predictive novelty.

We comment on cases in the history of Astronomy, which may shed some light on the current established but enigmatic concordance model of Cosmology. Should the model be understood by adding new entities such as Dark Matter and Dark Energy, or by modifying the underlying theory? For example, the prediction and discovery of planet Neptune can be regarded as analogous to finding a dark component; while explaining the anomalous perihelion precession of Mercury by General Relativity can be taken as analogous to the possibility that modified gravity is an alternative to dark components of the universe. In this paper, we revise this analogy coming from the history of astronomy with an eye to illustrating some of the similarities and differences between the two cases., Comment: 8 pages, 2 pictures, 1 table, to appear in the RAS journal Astronomy & Geophysics (2014)