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The cosmological constant and the emergence of the continuum

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Naturalness problems that could be signaling the necessity a completion of an effective field theory with the introduction of an otherwise overlooked ingredient. The cosmological constant problem can be seen as a signal that the EFT for gravity, general relativity, is not correctly including the gravitational properties of the vacuum. Starting from the discussion of the a possible solution to this naturalness problem for a cc-like term in a BEC analogue model, I will briefly discuss how this particular mechanism can be extended, albeit in a preliminary form, to more genuine quantum gravity models like GFT, connecting in particular the problem of the determination of the gravitational couplings (and hence the hierarchies involved) to the appearance of a semiclassical space-time