The Sciences

# The Landscape - For Real This Time

Cosmic VarianceBy cjohnsonAug 14, 2005 10:51 AM

A couple of weeks ago I used the phrase "The Landscape" in the title of a post but I was really referring to my garden, and I went on to mention there that I had deliberately chosen a misleading title for fun. Several people would not have known why this was misleading. I'd like to explain what I had in mind. This is also a continuation of the story I began in another earlier post concerning approaches to cosmology in string theory, the subject of the workshop I'm attending at the Aspen Center for Physics. (Cautionary note: I won't be able to include lots of details. This is meant to be a light sketch of some of the activity going on in the field, and some of the questions that have arisen, aimed at non-experts. Of course, I invite useful discussion of all levels in the comments.)

I'm going to assume that you'll recall the discussion from the earlier post, and the sketch to the right. The curve is a very simplified illustration of a very important point. It is the potential energy curve (I'll often just say "potential") for one of the scalar fields in the underlying theory, and it is hoped that almost all the scalar fields produced by string theory (showing up as one of the modes of the string, like all particles do in this approach to string theory) have a potential that is a bit like that. (I'll give you a geometrical picture of what a scalar field is, in a while, if you're not sure what that is.) There are two key features. 1) It has a nice well in the middle. This is where the scalar will like to settle, if anywhere near the well. 2) The value of the potential at the well (where the particle will settle) is positive. This positivity is important. Such positive contributions to the total energy of the system will break the underlying "supersymmetry" of the string theory, and give a postitive value for the cosmological constant. (This potential energy of the system is referred to as the "vacuum energy", being the "ground state" energy associated to universe thus constructed - this is the same as what a cosmological constant is, classically anyway.) We care about both of these because we know that the world is not supersymmetric (see the earlier post for what supersymmetry is) and because it is currently believed (and this may well turn out to be wrong (!) see Mark's recent post) that our world does have a positive cosmological constant. I should emphasize at this point that until recently, string theory studies have been mostly focused on models which were supersymmetric, in which case they have vanishing or negative vacuum energy (cosmological constant). A huge amount of knowledge and computational technques have been developed to study such cases. The possibility (and it is still just a possibility) that our universe might have a positive cosmological constant started a big discussion within the field about whether such vacua (solutions of the theory) could be reliably constructed within string theory, because it is very hard to do. I've already mentioned in the previous post that various scenarios (such as those of KKLT) were eventually presented for how such vacua could be constructed. The key ingredients are well-known. They are the "branes" (extended objects) of various sorts, and I also talked about those in that post. Let's move on a bit. What people are doing in the field now is exploring these constructions using the string theory technology we have available. The problem is that the computational technology is right at the edge of what we can do, and it is not easy to control these vacua. This means that people are still confused as to the reliability of the solutions that have been found, but - as far as is known - the basic scenarios which generate these sorts of solutions are very plausible indeed. Allied to that fact is the realization (pointed out first in this paper and explored and developed further in this paper) that there are very many vacua spanning rather closely spaced values of the cosmological constant. So there's a lot of choices, basically, and they look a lot like each other. So you might ask "why choose one over the other?". We'll come back to that in a bit. Within the limitations of the techniques that we have for exploring the contruction of these vacua it is now understood that there are vast numbers of these vacua, and a huge amount of them may have characteristics (such as the value of the cosmological constant) comparable to our world. So I promised in my most recent post that this would have something to do with mountains. Let's have a closer look at the picture I took up near the Maroon Lake earlier today:

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