Tuesday, January 14, 2014

A few more comments on inflation and the multiverse

[This carries on from a post yesterday where I attempted to explain what inflation has to do with a multiverse]

Is that it?

You might be thinking: "OK, that's a toy-toy model about how a multiverse might come from an inflationary model. Cool. But are there any non-toy models?"

As far as I'm aware, no. And this is where I definitely agree with Peter that, although it is certainly possible to generate a multiverse, it definitely isn't inevitable. In fact, if anyone reading this does know of any full models where a multiverse is generated, with a set of vacua with different energies, please let me know (even if it's just a complete toy model).

In which case, you might now be wondering why is there so much excitement amongst some cosmologists about multiverses? Why do some physicists want it so much? There are two reasons I can think of. The first is that the multiverse, coupled with an anthropic principle, can explain why the cosmological constant has the value it does. If the true model of inflation generated Big Bangs in many vacua (i.e. more than 10^130 vacua), then, even though most of them will have large vacuum energies, the Big Bangs that occur in them also can't support life. Therefore we would expect to find ourselves in a Big Bang bubble where the cosmological constant was small, but just big enough to be detected. And this is actually exactly what we see. [Edit: As Sesh points out in a comment, an additional assumption is required to conclude that the cosmological constant should be both small and measurable. This assumption is that the distribution of vacuum energies in the multiverse favours large energies. See the comment and replies for discussion. Thanks Sesh.]

The second reason multiverses are popular is that there is a candidate for where this absurdly large number of possible minima could come from and this is string theory. In fact, string theory predicts many more than 10^130 possible vacua.

Summary

So, that's it. A multiverse needs two things: a way that multiple possible types of universe are possible; and a way to make sure that these universes all actually come into existence. String theory suggests that there may indeed be multiple possible types of "universe" (i.e. sets of laws of physics), but it is eternal inflation that would cause many Big Bangs to occur and thus, potentially, to populate these "universes".

Some parting words...

There are some (perhaps even many) scientists who hate the idea of a multiverse and demand that multiverses are stricken from science for being "unfalsifiable" or "unpredictive" (because we can't ever access the other Big Bangs).

I don't understand this mentality.

Forgetting about whether a multiverse is "scientific" or not, what if it is true? What if we do live in a universe that, it just so happens, is part of a multiverse? Would we not want whatever method we use to try to learn about our existence to be able to deal with it? If we want "science" to be something that examines reality, then (if we are in a multiverse) should it not be able to deal with a multiverse? We might not be able to directly measure other Big Bangs, but we can infer their probable existence by measuring other things. [Edit(06/02): I just want to clarify that I'm not meaning to suggest here that science needs changed to be able to talk about untestable things, but instead that scientists are justified when trying hard to find ways to test this idea. And that there are ways to test it.]

Suppose we all lived 500 years ago and wanted to know why the Earth is exactly the right distance from the sun to allow life to occur. What explanations could we come up with for why this is true?

What is the real reason?

1. I have a question and a comment.

The question is about the line where you say "Therefore we would expect to find ourselves in a Big Bang bubble where the cosmological constant was small, but just big enough to be detected." Why should it be big enough to be detected? Why not orders of magnitude smaller than that? I think you've got another unstated assumption in there to come out with that conclusion.

The comment is about your parting words. I think you're misrepresenting the argument somewhat, in that if by measuring things in this universe we could learn about the multiverse, I doubt anyone would object to it.

Sure, maybe the multiverse is "true". It might be. But if nothing we can measure in this universe can possibly tell us whether it is or not, then it's an idea of zero intellectual value. It would be exactly equivalent to the argument that the earth is only 6000 years old, but God just deliberately put all those fossils in the rocks and depleted their carbon/uranium contents by exactly the right amount to make it look like the universe is old and evolution happened. That argument could also be true, but who cares? It is a complete waste of time to bother thinking about it. You would literally learn more about reality by studying theories that turn out to be wrong.

1. Regarding the first point. Yes, I agree. Thanks for bringing it up. The unstated assumption (as you know) is that the distribution of values of the vacuum energy in the multiverse favours larger values. This is what is expected though, because most fundamental physics theories predict vacuum energies that are similar to the energies of their interactions, which are much larger than our measured one.

Regarding the second point, I just don't think it is true that "nothing we can measure in this universe can possibly tell us whether [the multiverse] is true or not". The only thing that is true is that there is nothing we can do to get to one of the other Big Bangs. There *are* things we can measure in this universe to learn about a possible multiverse (for example, whether the inflationary potential that we come from has an eternally inflating region and has multiple vacuum states, or not - but I would claim there are other ways too) and people do still object to it.

But surely if we found out that the true inflationary potential was the two dimensional one I made up for part one of this post we could state with confidence that we do live in a multiverse, even if we can never interact with those other Big Bangs.

2. Ok, I guess I should clarify.

If we can measure things which tell us for sure that the inflationary potential has such-and-such a shape and therefore there will be other universes, fine. That form of the multiverse idea is falsifiable, insofar as the inflationary potential could be measured to have a different shape. I'm not sure anyone has a problem with that.

What people object to is using the idea of "a multiverse" in order to explain things in this universe. Until you can make sensible (i.e. falsifiable) statements about the laws of physics in these other universes, assuming they exist, I don't think you can use the multiverse to explain the laws of physics in this universe.

3. But isn't that the whole point of studying the multiverse (i.e. trying to understand what the laws of physics would be like in the other universes in order to make predictions about our own)? This is what people who "study the multiverse" are doing with their time (it's just really hard, (i.e. because string inflation is so hard and because of measure problems) so they're making really slow progress) and getting chastised by other physicists for doing!

Whether this is done in a bottom up sense (i.e. constructing a complete inflationary model with a set of vacua with different laws of physics and constructing a measure (I say constructing, but *maybe* the measure problem can be solved without observation) for how they are populated and then applying an anthropic cut to predict the probability distribution of observed values in our universe. then you measure those values and see if the observed values fit the prediction.),

Or in a top-down approach (i.e. the fact that if a multiverse does exist we should find many fundamental parameters that are close to catastrophic boundaries),

I don't see how that isn't science. I don't like the concept of falsification. The more sensible concept seems to be whether evidence can be obtained that would strengthen or weaken the likelihood that the model is true. If something can't be falsified, but evidence can be obtained that makes it more believable or less believable I still want people to be working on understanding that something. Finding more catastrophic boundaries strengthens the probability that the multiverse is true, even if not finding them doesn't "falsify" it. Also, if a multiverse is true, then finding where these catastrophic boundaries are would help the bottom up approach because it would indicate what sort of fundamental physics should be chosen anthropically. This would point where to look in field space for the correct inflation/vacua model.

I would totally agree that at the moment the multiverse is just a highly speculative idea, rather than a fully-fledged model, however I don't think that means the idea is "not scientific" or "not testable". Whether it is scientific is just semantics, but it definitely is testable.

2. I see the "falsification" part as sort of like arguing that since we can't measure an imaginary distance we should quit complex numbers until we find something we can use them for. Boolean algebra didn't have practical usability either when invented. So there's nothing wrong with building a model even if it can't be instantly validated *at the moment* because that's how you figure out how you could validate it - noodling with the model. The key is that you always remember it's not proven - just a model. The problem is that popular press have shown a lack of clarity and self-discipline to keep that difference listed as a fundamental part of the conversation.

1. I have to play devil's advocate here, because as I wrote in the post, I *do* think the multiverse is scientific. However, I think part of the objection people have comes from the fact that these other Big Bangs are entirely causally separated from us. It isn't a case of just waiting for technological improvements before we can wander over and look at them, we will *never* be able to observe any other Big Bang in this multiverse.

HOWEVER, I don't understand why this means we can't infer a multiverse's existence through other means. And here I agree with you, just because we are not in a position to immediately, or even quickly "falsify" something, doesn't make it not worth examining. There are cathedrals that took hundreds of years to build (and some still being built!!)! Science could use a little patience, so what if string theory/multiverses/etc don't get properly tested for 600 years, that doesn't make them not worth examining in a theoretical sense now. They might be true.

You might be right about the popular press, etc. While I do think the multiverse is worth examining, I don't think it is irrefutably true, and some of its proponents do present this perspective at times. Frustration with that, I totally understand (and share sometimes).

Thanks for the comment!

2. The Cologne Cathedral Was started in 1248 and completed in 1880. If, in 2600, the multiverse is still untested, then I will start to waver on whether it is "testable".

3. Hi Shaun,

Nice article! :-) I have two questions, though, and one comment.

The first is about terminology --- AFAIK, the term "Big Bang" denotes the "initial moment", or the "beginning of time", or more seriously the epoch of the Universe where quantum gravity effects were dominant, and where GR predicts the singularity. Everything else, including inflation, bubbles, structure formation, etc. happened *after* the Big Bang. OTOH, you seem to use the term "Big Bang" to denote a post-inflationary period of a given bubble-universe. Where did this usage of "Big Bang" come from? I've never seen it before, and I fear that it introduce a nontrivial confusion among people.

Second, regarding testability of multiverse models --- is there any experimental signature of the inflaton that can be used to test the multiverse hypothesis, other than explicitly measuring the potential curve? The latter is likely to be very hard, given that the inflaton field has not been observed directly at all. Arguably, its mass is very large, so we would need accelerators of energy higher than present 10TeV just to detect the particle, let alone measure the whole potential curve. So, does the multiverse provide any "smoking gun" prediction, in the sense that *any* theoretical model that contains that same prediction also necessarily predicts the multiverse?

Finally, I don't find your argument "different minima produce different laws of physics" to be very convincing. The value of cosmological constant notwithstanding, I don't see why any SM parameter has to change? Particle masses are dictated by the Higgs field, rather than the inflaton. The interaction coupling constants seem to be even more independent. Even if you take string theory seriously, so far it doesn't provide any direct connection between SM parameters and the landscape of Calabi-Yau compactifications. Outside of wishful thinking of type "maybe it happens", I don't see absolutely any argument (not even theoretical) that would indicate that inflaton vacua are connected to the values of SM parameters. It seems that the idea of level II multiverse requires much more work to be justified as a viable scientific scenario. So far, I see only level I to be supported by eternal inflation scenario, nothing else.

Best, :-)
Marko

1. Hi Marko, thanks for the questions and comment.

Regarding "Big Bang", other people have sometimes mentioned the same to me. I don't think the definition you are suggesting is particularly useful though. If that was what "the big bang" was then I doubt many physicists would feel confident saying "the big bang happened". I certainly wouldn't. The Big Bang model that people wrote papers on and has subsequently been tested relates to the rapidly expanding, hot, dense state of the early universe and its current observational consequences. You say you've never encountered my usage of big bang, but to be honest, I've rarely encountered the definition you're suggesting. The Wikipedia page seems to agree with me, going into all sorts of details of the formation of light elements, the CMB, etc, etc. Sure, people say "the big bang happened 13.8 billion years ago, but all that stuff *did* happen that long ago... even the CMB had formed within just 400,000 years, which is still 13.8 billion years ago.

Actually, reading more closely, the first few sentences of the "overview" part of the Wikipedia page seems to refer to exactly this dual use of the term, so I suppose it has been used in both contexts. However, I would guess that when most cosmologists use the term "the big bang" they mean the hot, dense, rapidly expanding state and not the initial singularity (or, they might include that singularity within the big bang, but it wouldn't be the entirety of what they mean by big bang).

2. Regarding your second question, not that I know of. The common feature of every inflationary model that can generate a multiverse is that they have this patch of the potential where eternal inflation can occur. However, that patch can be much further up the potential than the region that corresponds to the scales we can observe.

There are potential signals one might see if two or more bubbles collided early in their Big Bangs (using my definition ;-) ). If we were the descendants of such a collision we might see gravitational waves from such a collision and/or particular features in the CMB. If seen, that'd be a smoking-ish gun.

We could potentially measure, or at least infer, the full inflationary potential through cosmology though (i.e. we don't necessarily need a collider). If a model made a particularly precise set of predictions for observables relating to the primordial density perturbations, and temperature anisotropies of the CMB and the universe happened to satisfy those predictions it would be strong evidence that this particular model of inflation was correct. Most models, unfortunately, have too much freedom and one can change the values of their parameters in order to match many observations, but this isn't true for all. For example, the simplest potential $$m^2\phi^2$$, although plagued with theoretical difficulties, did make a prediction that the amplitude of gravitational waves and the way the amplitude of the temperature anisotropies changes with scale must satisfy some particular property (if you know what I'm talking about, essentially I'm saying that observations would have to show up somewhere on a line in n_s vs r space), if that had been satisfied it'd be pretty clear that model was correct (despite its theoretical issues). Unfortunately, that model is now all but ruled out. Some other models also make equivalently precise predictions though, so it's still a possibility that we'll know the full inflationary potential, in which case we'll know whether that potential supports eternal inflation.

3. Regarding your final comment, well, firstly, sure the masses of the standard model particles depend on the value of the Higgs field, but they also depend on the strength of the coupling between the Higgs field and the SM particles, which could depend on another field. And the Higgs vacuum expectation value itself could depend on the value of other fields.

As I wrote in the article, I'm unaware of any complete model of inflation that generates a multiverse, so you're right to say it is speculative; however the idea that more than just the vacuum energy would be different is a pretty robust part of that speculation. Normally it is used as an argument *against* the multiverse, because many other parameters in the universe don't seem to be near catastrophic boundaries.

You mentioned string theory and its landscape of vacua. If string theory is true, then the standard model particles *are* fields of string theory (they're not somehow embedded in a string theory background, they are of string theory themselves). Those many vacua of the landscape do have different laws of physics, sufficiently different in fact that the standard model is yet to be found in them (or at least was in 2010 when I worked in a department where people were looking for it). So it isn't just that different vacua will have different values of SM field parameters, in most vacua the SM fields aren't even there!!

Moreover, string theory doesn't have free parameters, so the couplings of whatever fields are in each vacuum (e.g. the Higgs field to the standard model particles in this "correct" vacuum) *must* be the result of the vacuum expectation values of other fields.

So, I guess I'd say there definitely is a problem, but it is probably the exact opposite to the one you suggest. The problem isn't "how do we know the SM particles have different masses, etc, in different vacua?" it is "how do we even know there is a vacuum that has the SM, let alone the SM with the correct masses and interaction strengths, etc).

I hope those answers helped in some way or another. :-)

4. Sorry, one last thing regarding "Big Bang", that wikipedia page seems to mix the definitions very liberally. In one sentence it writes "Though simple atomic nuclei formed within the first three minutes after the Big Bang" (my emphasis added), suggesting that the big Bang is only the singularity, but then later it goes out of its way to stress "The Big Bang theory does not provide any explanation for the initial conditions of the universe; rather, it describes and explains the general evolution of the universe going forward from that point on" (my emphasis added).

So, I don't know. I'll rest on my first comment, I don't understand the use of defining the Big Bang to just be that initial singularity, instead of all the interesting evolution after that, which we understand and have verified.

4. Hi Shaun,

Thanks for the replies! :-)

Regarding the definition of the Big Bang ---

"You say you've never encountered my usage of big bang, but to be honest, I've rarely encountered the definition you're suggesting."

Yes, I've seen the Wikipedia article on the Big Bang, but there are also other articles which clearly denote Big Bang as the initial singularity. For example, in

http://en.wikipedia.org/wiki/Inflation_%28cosmology%29

the very first paragraph states: "The inflationary epoch comprises the first part of the electroweak epoch following the grand unification epoch. It lasted from 10^{−36} seconds after the Big Bang to sometime between 10^{−33} and 10^{−32} seconds."

Or if you look at the article

http://en.wikipedia.org/wiki/Chronology_of_the_universe

there are references to Big Bang as a singularity all over the place. The very first paragraph says "The instant in which the universe is thought to have begun rapidly expanding from a singularity is known as the Big Bang.". Looking further down, they define the Planck epoch as "Up to 10^{–43} second after the Big Bang", then the GUT epoch as "Between 10^{–43} second and 10^{–36} second after the Big Bang", etc. For the inflationary epoch it is said "Unknown duration, ending 10^{–32}(?) second after the Big Bang".

On the other hand, the phase you define as the Big Bang is called the "reheating phase" in those (and other) articles, which happened (clearly) after the inflation phase.

My suggestion is that, if you continue to use your definition, you should clearly distinguish it from the other one, and warn your readers that there might be some terminology clashes around. Just to avoid confusion. :-)

Next, regarding your second reply --- thanks! :-) About bubble collisions, we'll just have to wait for the Planck polarization data to arrive. Which should happen this summer, if I'm not mistaken? :-)

Finally, regarding the SM parameters --- again thanks for the reply! :-) My (outsider) impression regarding the level II multiverse was that the idea of inflaton-dependent SM parameters was motivated primarily by string theory, to begin with. Unfortunately, as you say, string theory apparently failed to deliver anything even resembling the SM from the landscape. In that sense, the level II multiverse was motivated on a wrong premise, so to speak. So my question/comment was on the lines of --- is there any theoretical motivation for level II multiverse *independent* of the string theory landscape? If not, Occam's Razor would favor only the level I multiverse, with identical laws of physics everywhere, as the simplest theory. That's how I understand the state of the art, and consequently I'm quite confused why a whole community of scientists is getting so excited about the idea of level II multiverse. IMHO, it doesn't seem to be necessary in any sense...

Best, :-)
Marko

1. Regarding "Big Bang", it seems you're right. I'll do my best to be clear about this in the future. Thanks. I'm frustrated by this situation though because the way "Big Bang" is used to define a singularity I don't feel comfortable writing "The Big Bang happened", but that will make communicating the early universe tricky. Ah well, such is life.

Yeah, that's when I've been lead to expect new polarisation data too. I understand that they're having difficulties with it though :-/.

Finally, you write "string theory failed to deliver... the SM from the landscape" (my emphasis). I don't understand why people have such little patience. $$10^{500}$$ is a huge number. String theory has so far failed, but that doesn't mean the SM isn't lurking there somewhere. But yeah, in a world where string theory was not a compelling possibility for the correct description of nature, I would probably agree with you that Occam's Razor prefers identical bubbles. In fact, even if string theory is true, Occam's Razor probably prefers identical bubbles, because the most compelling models of inflation are all ones with identical vacua (so far). It would only *prefer* them though. The different physics vacua still seems like a compelling *possibility*, even if not preferred.

5. Hi Shaun,

True, maybe I was a bit too harsh to say that string theory failed to deliver. I agree that SM can yet be found in string landscape. It's just that the search for it has been withering away in recent years. The string theorists all but stopped looking for a correct compactification, AFAIK...

Anyway, thanks for the discussion, and an interesting article, I enjoyed it a lot! ;-)

Best, :-)
Marko

6. Shaun,

Given your discussion with Marko, why does Linde (and the rest) present the Level II multiverse as so necessary and certain?

-joepro

1. Hi Joe, thanks for the comment (and thanks for reading all the way through the comments!).

I honestly don't know. I think it is a fairly rational belief to have that most inflation models will have regions that support eternal inflation and thus will produce a multiverse of bubble universes. However, most of those models will also only have the one, unique vacuum. I guess this would be a Level I Multiverse.

Linde (and the rest) are then just assuming that any complete model of fundamental physics will allow for the post-inflationary universe to fall into non-degenerate vacua. However, even if string theory is true, and there are many vacua, it doesn't seem inevitable to me that the post-inflationary universe can populate them.

I'm actually unaware of *any* model that populates more than one vacuum and is consistent with all observations.

7. Shaun,

Your descriptions make sense and I (for the first time) can see how an inflating universe can produce many bubble universes that are kept apart by inflation. But these bubble universes are not coming from each other' they are coming from the original inflating universe.

Linde seems to be saying that the bubble universes give rise to other bubble universes (or at least that the original inflating universe gives rise to other infalting universes). However, if that is so, it seems like they would bump into each other all the time, assuming they all stay in our 4 dimensional space time, which I think he says they do.

Does the answer have something to do with the vacua you addressed above?

It that what I'm missing in Linde's explanation, or what?

-joepro

8. I think i've finally figured out what Linde is saying. Here's the way i understand it.

The universe inflates very rapidly for just a very small fraction of a second. Then it stops and inflates much slower. In many regions it stops and releases dark energy into particles and starts a big bang bubble universe there. But other regions start inflating fast agsin, thus giving rise to "new" infating universes. But they are really just a part of the same space time that's inflating fast again, pushing away the other parts of space time.

Linde claims that there might have been a initial start or it could go back indefinitely. I personally think it would have had to start with an initial universe expanding.

-joepro

1. Hi Joe,

Yeah I think you've basically got it. If you have an inflating universe, in some regions of the total universe, eventually inflation will end, and you get all the things we associate to the ordinary big bang (formation of the light elements, the CMB, galaxies, etc), in others, inflation will proceed. But, in that bit of the universe that is still inflating, the rate of accelerated expansion will differ from point to point. If you have some patches that are accelerating at a much faster rate, they will eventually come to dominate all of that inflating patch, essentially forming their own "bubbles".

You would be right to think that, at the edge, of those bubbles all sorts of interesting collisions might occur; however, deep within these patches, the accelerated expansion means you will never see the edge (because it is receding from you, due to the expansion of space, faster than you can every travel to reach it).

Don't forget that the 3-d volume of the universe isn't conserved, so even though one inflating patch might be completely bounded by other stuff, the total volume inside the patch can continue to increase exponentially without "building up" against the edge.

(I hope this is helping, it's tricky to put into words in a comment at a blog!)

2. Concerning the new question you're asking, which is how the first bit of inflating universe got started, all I can say is that you've come across one of the biggest problems/issues of inflation.

If you have a nearly homogenous, expanding universe, then inflation can get started and then you get eternal inflation and everything that comes with it. But, inflation was supposed to be the theory that solved that problem and explained why we had a nearly homogeneous, expanding universe!

There are people trying to tackle these problems through arguments that are basically just slightly more sophisticated forms of saying "well, inflation starting is incredibly improbable, fine, but once it does start, eternal inflation means that anywhere that inflation does, miraculously manage to get started, will come to dominate the rest of the universe (in volume), therefore you always expect to be a descendant of an inflationary universe"... but these arguments are difficult and run into issues when taken to their logical conclusions. You might find some insight in this article from Sean Carroll?

3. Still, humanity doesn't need to solve all problems at once. So, if the observational evidence points towards inflation being the origin of our universe (and so far it seems it does), we can acknowledge that and study the *consequences* of an inflationary epoch, without having yet solved the problem of the *origin* of an inflationary epoch itself.