ask a physicist

[freyar]

Ok. Quick question for you:
One of the big problems with the dark energy/cosmological constant component of the universe is explaining its value-- when I was in grad school the best models from particle physics proposing a nonzero vacuum energy were still 30 orders of magnitude off from the observed cosmological value.
Has string theory made any progress in the past 10 years on this problem: a reasonable value for the vacuum energy density?
Ben

There's lots and lots to say on this subject, but I'll try to avoid writing a book and just stick to the idea of vacuum energy.

Here's the background for the question: The universe is expanding, and through the mid '90s, everyone expected that the expansion should be slowing down due to the gravitational attraction of all the stuff in the universe. Then two different research groups independently showed that the expansion is actually speeding up. This requires some kind of unusual physics to explain, and the simplest explanation is that there's a cosmological constant term in the Einstein equations of general relativity. This term is also how vacuum energy, or the energy of empty space, would appear in the Einstein equations. Vacuum energy is interesting because, as space expands, the density remains constant, so the total energy goes up. This property makes the expansion of space speed up. Of course, there are other ways to get the universal expansion to accelerate (which as a whole are given the name dark energy), and I'm happy to talk about those, but I'm keeping to vacuum energy here.

The problem with vacuum energy (known as the cosmological constant problem), as fuindordm indicates, is that rough estimates of it from particle physics calculations give a ginormous number, around 120 orders of magnitude too big (that is, 1 followed by 120 zeros times the actual number). Until the discoveries of the accelerating expansion, most physicists believed there must be an unknown physical principle that sets the cosmological constant to exactly zero, since making something so much smaller than it "should" be but not actually zero seems like quite a tall task (indeed, many people who believe in other forms of dark energy at least implicitly believe the cosmological constant is zero even now). This latter, more difficult situation is the one we ended up with. How do you make something so much smaller than it "wants" to be?

So, what ideas do we have (especially from the last decade or so) from string theory? One possibility is a "string inspired" idea that uses extra dimensions. The essentials are that all the normal matter (and probably dark matter too, I'm not that sure of those details) are stuck to objects called branes (short for membranes), which have the usual 3 spatial dimensions. But there are also 2 extra dimensions perpendicular to the branes. There can be a large vacuum energy on the branes, but, instead of causing our space to expand faster and faster, it causes the extra dimensions to curve (into a shape like an American football or rugby ball). There are some people who really really love this idea, but not a lot of people are sold on it (at least, not a lot of people have worked on it). Part of the reason is that it seems like it shouldn't work in the end for some technical reasons. In fact, I saw a paper the other day arguing that this idea is fatally flawed.

The main development on the cosmological constant problem in recent times came up in 2003 and involves the (weak) anthropic principle. The anthropic principle says that, if a universe can be observed, it must be capable of supporting intelligent life that can observe it. The point is that the vacuum energy must be incredibly tiny for stars and galaxies (and presumably therefore life) to form. In fact, the maximum possible value for the vacuum energy is not much higher (maybe a factor of 100) than that observed, and Steven Weinberg (a Nobel-winning particle physicist) actually predicted the discovery of the cosmological constant based on these anthropic arguments back in the 1980s.

Where string theory comes in is to provide a mechanism to work. You see, for the anthropic principle to make sense as a physical principle, you need a universe where there are lots of different regions of different effective vacuum energies; this is often called a multiverse. To get this, you need a theory with a lot of different states of different vacuum energies and a way for the universe to transition in between them. About 12 years ago, string theorists working on problems about moduli fields (see the Ant-man answer above) discovered that string theory apparently satisfies both of these properties. In other words, it looks like string theory automatically gives you a multiverse. Since then, there's been a lot of work on understanding what the probability is that we'd live in a part of the multiverse with our value of the vacuum energy. This is kind of tricky, since it's hard to come up with a mathematically rigorous definition of probability that applies to chunks of an infinite universe.

This idea is pretty polarizing. A lot of physicists think the use of the anthropic principle is a cop out. Some of them have argued that there are technical (read as "highly mathematical") reasons to think that the calculations suggesting a string theory multiverse are subtly wrong. On the other hand, as witnessed by the amount of work in this area, a lot of people think this use of the anthropic principle makes sense and seems to fall out of the mathematics of string theory. The divide is partly, but not entirely, by age, with younger physicists a bit more in favor of anthropic arguments. Full disclosure: I think anthropic arguments are perfectly legitimate and have worked on multiple parts of this story. I'm also fairly sensitive to the technical questions raised by "anthropic opponents" and am perfectly willing to admit that there could be a subtle reason some of the calculations don't work the way they appear to. In any case, I think if you polled string theorists, you'd find a pretty significant split on whether the multiverse is a good/correct solution to the cosmological constant problem or not. And that's where we stand on vacuum energy (leaving aside other models of dark energy).

 

[fuindordm]

Thanks for the update! I'm interested in hearing more about the string theory version of a multiverse.

As I recall, another possible multiverse model was 'eternal inflation', which only requires a vacuum field and not string theory.

(Aside for the benefit of others) Inflation was a very short segment of time prior to what we usually think of as the Big Bang, when the universe expanded at an exponential rate rather than just a polynomial rate. This was a clever idea proposed by Alan Guth in 1981 which solves several problems of observational cosmology, such as "why is the universe flat" and "why is the cosmic microwave background the same temperature in every direction, even though wide angles were too far away from each other to come to thermal equilibrium when the background was created?" If you accept inflation, then the next natural question is "why did inflation stop", and the answer is that the high-energy field that causes inflation is still subject to random fluctuations in temperature, and eventually it cools enough to undergo a phase transition into a more "normal" set of particles and fields.

But why stop there? If we can imagine a pre-universe that was undergoing exponential inflation, it makes just as much sense to imagine that only small "bubbles" of the field undergo the phase transition to normal space. So the eternal inflation model is one where a real infinitude of "space" is filled with this inflationary field, and is eternally expanding at an exponential rate, but small regions of it are eternally cooling down through random fluctuations into regimes where field transitions to normal space. Each bubble undergoes its own Big Bang, but since a Big Bang only expands at a polynomial rate, the new universe never takes over (or even catches up with) the inflationary field that spawned it. Viewed from the expanding reference frame of the inflationary field, these bubbles quickly shrink down to nothing. Unfortunately, it's a multiverse model that really offers no hope of ever meeting our evil twins.

I don't think this model requires string theory, but it is similar enough in outline that we might be talking about the same thing. It is certainly a model that supports the weak anthropic principal, and I agree with you that the principal is reasonable provided we can make a strong case for a multiverse.

So is this the kind of multiverse that string theory supports? There are also cyclical multiverses (I vaguely remember a scale inversion principal of string theory, which implied that a universe that expands too far is equivalent to a universe that had shrunk too small), dimensional multiverses (different branes?).

 

[Umbran]

Inflation was a very short segment of time prior to what we usually think of as the Big Bang

There is no spacetime to inflate prior to the Big Bang.

Everything else works, though - inflation happens after the BB (from 10^−36 seconds after the Big Bang to sometime between 10^−33 and 10^−32 seconds), and there's a phase transition... but not everywhere. If the phase transition happens in bubbles, you get islands of what we consider normal space, separated by *vast* stretches of nothingness.

Though, with an infinite space, you don't really need that. In an expanding universe, you have bubbles of visible universe that'll never communicate anyway.

 

[freyar]

More on the multiverse later, but I quickly wanted to clear up a confusing bit of terminology.

Inflation was a very short segment of time prior to what we usually think of as the Big Bang

There is no spacetime to inflate prior to the Big Bang.

There are actually two slightly different meanings of "Big Bang" in physics, which are often not carefully disambiguated (to borrow a term from wikipedia).

One common one, which Umbran seems to be using, might be specified as the "Big Bang Singularity," meaning the beginning of space and time. There is literally no time before that. This is a singularity in general relativity but might be smoothed out in some theory of quantum gravity, like string theory. There is some but not a lot of research on fixing the Big Bang Singularity in string theory. I've done a little bit of work related to that.

The second common definition, which I think fuindordm is using, is often called the "Hot Big Bang." This is the period in the early universe (after the period of inflation fuindordm talked about) when there was a dense hot plasma of stuff. This is, for example, when the different isotopes of the light elements are formed (this is called Big Bang Nucleosynthesis).

Anyway, I hear and use "Big Bang" both ways, and it's an understandable confusion.

More of a substantial answer either tonight or tomorrow on the multiverse.

 

[Umbran]

The second common definition, which I think fuindordm is using, is often called the "Hot Big Bang."

Yeah. I never liked this terminology, *because* of the ambiguity it creates. It confuses laymen.

 

[fuindordm]

You're right, I was referring to the beginning of the hot dense phase, because anything prior to that doesn't have direct observational support. The singularity is an extrapolation, and most astrophysical cosmologists (as I was) do not include it in polite conversation.

 

[freyar]

Yeah. I never liked this terminology, *because* of the ambiguity it creates. It confuses laymen.

You're right, I was referring to the beginning of the hot dense phase, because anything prior to that doesn't have direct observational support. The singularity is an extrapolation, and most astrophysical cosmologists (as I was) do not include it in polite conversation.

Well, the problem is that the phrase was never defined precisely in the first place and was in fact coined as a derogatory for the idea by Fred Hoyle, who believed in steady state cosmology. The real issue is that, until the '80s or '90s, inflation wasn't part of the standard cosmological picture. So the Big Bang Singularity was immediately followed by the Hot Big Bang phase. It was all mushed together, and both uses stuck. And, as fuindordm notes, the singularity isn't really something we even really know is there.

 

[freyar]

Back before that sidetrack on nomenclature, we were talking about the multiverse and such...

Thanks for the update! I'm interested in hearing more about the string theory version of a multiverse.

As I recall, another possible multiverse model was 'eternal inflation', which only requires a vacuum field and not string theory.

(Aside for the benefit of others) Inflation was a very short segment of time prior to what we usually think of as the Big Bang, when the universe expanded at an exponential rate rather than just a polynomial rate. This was a clever idea proposed by Alan Guth in 1981 which solves several problems of observational cosmology, such as "why is the universe flat" and "why is the cosmic microwave background the same temperature in every direction, even though wide angles were too far away from each other to come to thermal equilibrium when the background was created?" If you accept inflation, then the next natural question is "why did inflation stop", and the answer is that the high-energy field that causes inflation is still subject to random fluctuations in temperature, and eventually it cools enough to undergo a phase transition into a more "normal" set of particles and fields.

But why stop there? If we can imagine a pre-universe that was undergoing exponential inflation, it makes just as much sense to imagine that only small "bubbles" of the field undergo the phase transition to normal space. So the eternal inflation model is one where a real infinitude of "space" is filled with this inflationary field, and is eternally expanding at an exponential rate, but small regions of it are eternally cooling down through random fluctuations into regimes where field transitions to normal space. Each bubble undergoes its own Big Bang, but since a Big Bang only expands at a polynomial rate, the new universe never takes over (or even catches up with) the inflationary field that spawned it. Viewed from the expanding reference frame of the inflationary field, these bubbles quickly shrink down to nothing. Unfortunately, it's a multiverse model that really offers no hope of ever meeting our evil twins.

I don't think this model requires string theory, but it is similar enough in outline that we might be talking about the same thing. It is certainly a model that supports the weak anthropic principal, and I agree with you that the principal is reasonable provided we can make a strong case for a multiverse.

So is this the kind of multiverse that string theory supports? There are also cyclical multiverses (I vaguely remember a scale inversion principal of string theory, which implied that a universe that expands too far is equivalent to a universe that had shrunk too small), dimensional multiverses (different branes?).

We can start with another nomenclature issue, I guess. There are some people who use "multiverse" to refer to different types of particles living on different branes in different parts of the extra dimensions, but that doesn't fit the usual definition of multiverse because these different particles interact with each other gravitationally. While you're also right that there can be cyclical models of cosmology, I'm not aware of one that really qualifies as a multiverse. The typical definition of multiverse is a "large" universe where there are different (separated) regions with different physical laws (ie, different field/particle content, though basic principles of quantum mechanics still apply everywhere), large parts of which are out of (causal) contact with each other.

In any case, the "string theory multiverse" I talked about before is of this eternal inflation type that fuindordm describes. What he describes is a multiverse/universe where most of space keeps expanding exponentially fast with "pockets" of normal expansion, but all those pockets have the same physics, in particular the same vacuum energy. If we want to explain the small value of the vacuum energy, though, we need pockets of normal expansion with different physics than each other. In other words, the overarching theory needs (very very very) many states with different values of vacuum energy in each one. You certainly don't need string theory to have this structure --- this is a complicated but reasonable model just to make up from scratch --- but any model you do make up should eventually come from some theory of quantum gravity. The fact that string theory, which is a theory of quantum gravity (and everything else), apparently does give you just this structure of many states of varying vacuum energies is a strong motivation and is what led to the recent interest in these multiverse/anthropic models.

There is one other small difference compared to what fuindordm describes. In modern/stringy multiverse models, the transitions are not just from inflationary expansion to normal expansion, but mostly between regions with inflation at different rates. Of course, there are additional technical details --- for example, in this type of model, our pocket of the universe is created as a bubble in the eternal inflation that then undergoes a more standard type of inflation that heats up. But now, we see that the expansion of space in our region is starting to accelerate, so we might be entering another phase of inflation (just a very slow one). So we also experienced a transition from inflation to inflation, just with some more complicated intermediate stage in between.

 

[rknop]

Re: the name "Big Bang", here is an article I wrote nearly a decade ago back when I was an active blogger about why it's a bad name for the theory. Here, I'm talking about what freyar calls the "Hot Big Bang". I come from an observer's bias, so that's what I tend to think of as "The" Big Bang nowadays, rather than the initial singularity that comes out of General Relativity (while ignoring quantum mechanics).

 

[Scott DeWar]

What would happen if you shot a gun in space?