Author: Sean Carroll

Greetings from Baltimore, where I just gave a talk on the accelerating universe at Johns Hopkins. (After giving a similar talk at Penn the day before, and Urbana last week, and Brandeis and Arizona the week before that. I have to start increasing my speaker fees [from zero] or this will get ridiculous.)

Our universe is accelerating and we don’t know why. So my talk goes through a little flowchart of all the possibilities, similar to the approach in this paper. The leading candidate, of course, is a small vacuum energy, or cosmological constant — a tiny, persistent energy density inherent in space itself, rather than being associated with some particle or field. But this possibility raises two huge questions: why is the vacuum energy much smaller than it naturally should be (by a factor of 10^-120), and why is the vacuum energy density comparable to that in matter today, even though they evolve rapidly with respect to each other as the universe expands?

What everyone would like to have is a formula that predicts the correct value of the vacuum energy in terms of other measured quantities. But we don’t seem to have any clue how to find such a formula, or even if it exists. So various people (I don’t know the history well, so won’t attempt to attach names to ideas) have suggested that the vacuum energy is not a constant of nature, but rather an environmental variable that can be different from place to place in the universe. It seems quite constant over our observable universe, so this scenario needs to posit the existence of regions of space far outside our observable universe, which we can’t see and which have very different conditions. The part of the universe that we observe is certainly finite, but it’s quite big — tens of billions of light-years across. Still, there’s nothing to stop us from imagining other regions, just as big, which are outside what we can observe — it would be inappropriately anthropocentric to imagine that the entire universe resembles our little piece of it.

So the idea is that the vacuum energy is a consequence of local conditions, rather than a fundamental number — much like, for example, the temperature of the Earth’s atmosphere. If we imagine some primitive physicists living in a region of Earth that was perpetually cloudy and with a very mild climate, they might expend a great deal of effort trying to predict the temperature from a theory of everything. But we know better; outside the atmosphere the temperature is very different. Further, we are not really surprised to find ourselves here on Earth, rather than on the surface of Saturn or the Sun, even though the Earth is quite tiny compared to them; the conditions are just more hospitable here.

Likewise with vacuum energy. If the vacuum energy were very large and positive, life could not exist, since the huge acceleration that would result would make it impossible for individual atoms to form, much less stars and galaxies. If the vacuum energy were large and negative, it would likewise squeeze things together, collapsing the entire universe in a tiny fraction of a second. From this point of view, it’s not a surprise that we measure such a mild vacuum energy — if the magnitude of the vacuum energy were anywhere near its “natural” value, we would not be here to measure it.

Of course, it’s never a surprise to find that a quantity takes on a value that allows us to exist — it’s kind of necessary, when you think about it. The question is, did we just get lucky enough that it worked out that way, or does this true statement actually count as an explanation for something? If our observable universe is just a small patch of a larger ensemble in which the vacuum energy takes on all sorts of values, there is no point in looking for a unique formula that determines its observed value; we are constrained to measuring only those parts of the ensemble that are hospitable to the existence of intelligent life. This approach to understanding the vacuum energy or other constants of nature is sometimes called the anthropic principle (and sometimes called other things, so please let’s not argue about the terminology).

I don’t think anything I have just said should be controversial in any way; it’s essentially a long string of tautologies. Nevertheless, people get rather emotional about this issue. Some folks are quite fervently in favor of the anthropic approach, some are equally strongly against it. I find myself disagreeing with just about everybody.

For the people who like the anthropic approach, it’s necessary to believe that there really are all those regions of universe out there with different values of the vacuum energy (and presumably, of all the other parameters of physics). Remarkably, this is not an implausible idea. Our best candidate for a reconciliation of gravity with quantum mechanics is string theory, which predicts that there are really eleven dimensions of spacetime. We look around and only see four dimensions, so the extra ones are somehow hidden — probably by being “compactified” into a tiny ball that is so small we can’t see it. Each different way of compactifying would give rise to different physics in four dimensions, including a different value of the vacuum energy. How many different ways might there be? This is currently under investigation, but the numbers being bandied about look like 10⁵⁰⁰ or worse. (For purposes of comparison, the number of particles in the observable universe is only 10⁸⁸.) So, many different compactifications, and likewise many possible values of the vacuum energy — that’s the celebrated “string theory landscape.” But that doesn’t do us any good unless those possibilities are actually realized somewhere out there. No problem; inflation allows us to take a tiny region of space and boost it up to a universe-like size. Therefore it’s by no means impossible that the combination of inflation and string theory has indeed given us a huge collection of many different “universes” with different values of the vacuum energy.

Of course, there’s a long road from “by no means impossible” to “likely true.” The fact is we understand precious little about the string theory landscape, and not that much about the process of inflation. Even if we did, we’re pretty clueless about how to turn such an understanding into a computation of what the vacuum energy should be. The problem is that we’d like to know what a “typical observer” in this baroque ensemble of universes is likely to measure. That’s nearly hopeless, as we don’t know what “observers” would be like if the laws of physics were dramatically different. Since what we actually want to do is hopeless, some people try to do a much simpler thing, which is just to count the number of vacuum states with a given vacuum energy. That’s nice, but unless we understand all of the physical process in these states, we don’t know what “life” would be like there. Not to mention that the total number of observers in the entire spacetime is likely to be infinite.

So, even if the anthropic principle is right, in the sense that our observed vacuum energy is simply an environmental variable whose observed value can be attributed to anthropic selection, we’re extremely far away from being able to use such a scheme to predict anything. People try, but I don’t think the results should be taken seriously at this point.

On the other end of the spectrum are people who think the whole idea is completely non-scientific, or even anti-scientific. As far as I can tell, their objections generally come in two forms — either that it’s “giving up” to attribute the observed value of a parameter to a selection effect rather than as derivable from the laws of nature, or that all these extra universes are unobservable in principle, therefore shouldn’t count as part of a truly scientific description of the world.

I honestly don’t see why either objection makes sense. The fact is, those extra parts of the universe might really be there, whether we can observe them or not. And if they are, it’s completely possible that the vacuum energy really does change from place to place, rather than obeying some fundamental formula. To me, science doesn’t proceed by first deciding how the world works, and then forcing it to conform; we keep an open mind, and try our best to understand how our actual universe behaves. If our best theories predict that the universe has very different conditions outside our observable patch, and that there is no unique prediction for the vacuum energy, than we have to learn to deal with it, even if those conditions will never be directly observed. The universe doesn’t really care how we would like it to behave.

Of course, that is no reason to give up the search for a more traditional calculation of the value of the vacuum energy. As I just said, we are extremely far away from having any confidence that there are multiple domains, and even farther away from using that knowledge to reliably predict anything. We don’t usually accuse our fellow scientists of “giving up” on one hypothesis whenever they propose an alternative; we usually have lots of different hypotheses floating around, and try our best to see which ones work and which ones don’t. There is plenty of real science remaining to be done before we have any reason to accept the anthropic idea to the exclusion of others — we need to verify that the dark energy is truly constant rather than dynamical, we need to search for supersymmetry and extra dimensions at particle accelerators, we need to develop our theoretical understanding of string theory and inflation to the point where we can begin to make sensible predictions. The great adventure is far from over — it’s very much in full swing.