Geometric fine-tuning?
When astronomers put their telescopes to the skies, they find that the Universe looks pretty much the same in all directions. In technical terms, it is said to be isotropic. That is odd, for the mathematics describing the Universe allows for it to be so vastly different from that! In fact, an isotropic universe is a very special universe. How did the Universe come to be so special? One strategy that might bypass the problem, is the very forceful theory of inflation. This theory solves the so-called 'horizon problem' (why does the radiation we receive in our telescopes have essentially the same temperature, independent of the direction?!) and the so-called 'flatness-problem' (why is the Universe so flat?!). Coarsely, inflation says that the Universe looks very flat and boring and ‘well-tempered’ because it was once very small, before it all of a sudden expanded extremely rapidly. So, much like the earth looks flat when you look to any direction from a tall building, the Univese will look flat when we look around with our telescopes. Adding inflation to the equations might be the right guess (then again; it might also not be), but it is nevertheless ad-hoc. Anything ad-hoc deserves better attention. Hence we approach the problems of modern cosmology from an altogether different route, inspired by a different, but perhaps related, question: Is the Universe we observe likely? The answer to this question heavily depends on the kind of matter content existing in the Universe. Modern cosmology is based on the so-called concordance model (LCDM). To date, we seem to have no other theory describing all the observable Universe as precisely as this model does. Paradigm established.
We go the other way. By ridding the theory of the assumptions made by physical cosmology concerning isotropy, we ask instead how likely an isotropic universe is in the first place, given the theory. That is: we take the concordance model (or any other model) and situate it in the broader mathematical context of General relativity, to see how the fuller theory tosses and stretches it around. In technical terms, we study the so-called Bianchi models, which comprise the set of (simply transitive) fully anisotropic initial conditions for our Universe. What do we find?
Check out our (peer reviewed) publications on the topic:
[1712.08752] Bianchi cosmologies with $p$-form gauge fields (arxiv.org)
[1911.05793] Extended FLRW Models: dynamical cancellation of cosmological anisotropies (arxiv.org)
Why this research?
Consider for a moment the hypothetical scenario where it turns out that the Universe in which we find ourselves is found to be infinitely unlikely from a theoretical point of view. Now that would be a curious thing, wouldn’t it?