Today I posted a version of the talk I gave at LOOPS 13 to the archive (1308.2934). You can also see the original slides. In principle this will be a longer paper soon, but I have some new ideas after my attendance at LOOPS 13 and I’d like to add them before doing something official.
Basically, classical gravity has nothing to say about the topology of the universe, and one would hope that quantum gravity would. By topology of the universe I mean large-scale structures – general relativity actually can’t tell if the universe is a sphere or a torus, but it can tell us that it appears to be locally flat. There could be any arbitrarily many numbers of “holes” in the universe, as long as the universe itself and the holes were both large enough that things still look flat in our little piece of things.
This means that we have to specify (read: put in by hand) the topology of the universe. Maybe not such a big deal since the model seems very good, but if quantum gravity is really “fundamental” then we don’t really like having to tell it what to do. Since there are a large number of different options for the topology (something like “as many integers as you can count”) specifying one in particular seems a bit strange. It’d be really nice if quantum gravity told us which one is the correct one – and even better if it matched observations!
That’s what my current work is focusing on, which started with an idea from Denicola, Marcolli, and al-Yasry (1005.1057). Without more details, the basic idea is to modify a current approach to quantum gravity (loop quantum gravity) to include topological data. That would allow us to ask questions about the topology, like “where did it come from?” and “what topology do we predict the universe to have if this theory is correct?” At this stage we are just checking to make sure the various constructions of LQG still work, and in this paper I am showing how to actually calculate some topological information. Hopefully this will lead to some calculations which show that LQG a) does include topological information, and b) predicts the topological structure of the universe.