We had a really interesting discussion of the quantum physics of de Sitter spacetime yesterday here in Aspen, starting with a review of the behaviour of scalar fields in such a background, led by Don Marolf, and then, after lunch, an open-ended discussion led by Steve Shenker. This is all quite difficult, and is of course quite relevant, since a piece of de Sitter is relevant to discussions of inflation, which seems (from cosmological observations) to have been a dominant phase of the very early universe. As the most symmetric space with positive cosmological constant, de Sitter may also be relevant to the universe today, since dark energy (first recognized after 1998’s observations of the universe’s accelerating expansion) may well accounted for by a positive cosmological constant.
So we need to understand this type of spacetime really well… and it seems that we don’t. Now there’ve been a lot of people looking at all this and doing really excellent work, and they understand various issues really well – I am not one of them, as I’ve not worked on this in any detail as yet. Do look at the papers of Marolf, and of Shenker, and collaborators, and references therein, and catch up with what’s been going on in your own way. For what it is worth, the sense that I get is that we’re trying to solve very difficult issues of how to interpret various quantum features of the spacetime and getting a lot of puzzles by trying to make it look a lot like things we’ve done before.
Now, we may solve all these puzzles…. but my current take on this all is that we’re missing something really key. I think that we’ve not completed the job of formulating quantum theory. This is more than just saying blandly that we don’t understand quantum gravity fully. I think that we’ve learned a lot about quantum gravity from string theory, but I think we’ve been fortunate – and perhaps a bit spoiled – with the progress we’ve made in spaces with zero cosmological constant and negative cosmological constant, which gave us great insights as to how to deal with perturbative gravitons, and huge chunks of the non-perturbative story, leading to things like AdS/CFT and gauge/gravity dualities in general (with the rich set of applications and techniques that I’ve mentioned here a lot)). But I am not so sure that de Sitter (and hence cosmological and related matters) is going to go through without us radically re-thinking what we even mean by some of the things we routinely do in quantum theory, and probably enlarging the toolbox somewhat. When I say radical, I’m thinking that we may need totally new rules, perhaps as fresh to us now as the ones that were needed back in the early parts of last century when we were trying to make sense of interpreting and predicting the results of the experiments back then, leading to modern quantum mechanics and ultimately the relativistic quantum field theory that we use routinely today. Those rules were developed in a way that allowed us to treat spacetime as a well-behaved bystander, and the later work we’ve done in string theory allowed us to continue to make great progress, even allowing the spacetime to be more than a bystander… but still well-behaved, with nice asymptotic regions that look safe and familiar, and perhaps above all – stable. The point is that de Sitter is not a nice bystander at all, so why are we sure that our most basic rules of quantum theory are complete enough for the job of understanding it? (I mentioned this near the end of the discussion. The good news was that I was not burned at the stake…)
I’m not saying I have any answers yet. I’ve been mulling over this and related issues for a number of weeks now, and I have not yet found a good setting to try out the one cool – but highly speculative – idea I have so far. The only thing I’m fairly sure of is that we’ve to make a whole bunch of conceptual leaps to complete the story, not just tinker with the things we already have understood (although, of course, you have to start somewhere, so kudos to those at the coalface doing hard work with the tools we have in work that will surely help show the way…)
I think this means that there are exciting times ahead!