As you may know from three previous recent posts on research (here, here, and here), I’ve been thinking and calculating a lot in the area of dynamical cosmological constant – concerning mostly (but not entirely) thermodynamics and quantum gravity. Specifically, the cosmological constant becomes the pressure variable in the thermodynamics. I think it is important, and will teach us something about things like gauge/gravity duality, string theory, black holes, and perhaps even cosmology, but I am not sure what yet. I’ve made some suggestions in recent papers, and computed some interesting things along the way.
Anyway, the larger community has not been following this story much, since: (1) It means a break with some powerful and still very fruitful frameworks where the cosmological constant being fixed is a given – like AdS/CFT – and it is not clear what that means yet, so the motivation is not super-strong; and (2) Let’s be honest, there’s no superstar working on it, so it is not going to get anyone any points. So I’ve been trying to shout about it in my little way from the periphery, as I think it might be useful, and since several people have been doing really good and interesting work on this issue for many years and it is worth more people seeing what they’ve been up to.
So imagine my pleasant surprise when I looked on the listing of new papers on the arXiv for today and saw three (!) papers on the subject, moving things forward in various ways. (They all seem to have noticed some of what I’ve written and cited it too, which is awfully kind.) It all looks interesting: There’s the paper by Grumiller et. al., working in two dimensional dilation gravity, the one by Frassino et. al., studying Lovelock gravity, and the one by Dolan, in five dimensions, which seems to be trying to make more explicit an idea I’ve been thinking about concerning getting to grips with having a chemical potential for the number of degrees of freedom in a gauge theory (as measured by some power of N, the rank of the gauge group). The point here (see my holographic heat engines paper) is that pressure – and hence cosmological constant – is connected directly to N, and hence its conjugate, volume, ought to be this chemical potential. What is the best way to think about such an object in a field theory?
[Er..., the random drawing at the top has no connection to the post. I flew back from Newark to LA on Saturday and did my usual (as you may know from some previous posts of mine) practice of flipping through the airline magazine for an interesting face to do a bit of drawing practice with. This one struck me as an interesting face, and so I did some pencil work, followed by ink work, and then threw on a little watercolour. It was a challenge at several points since the plane decided to shake a bit every time I tried to work on crucial bits like eyes and lips... sigh.]