A new cosmological coincidence problem?

One of the consequences of the BICEP2 data from last week, should it hold up to scrutiny, and be seen by other experiments (I hope it holds up to scrutiny and is seen by other experiments), is that there is a significant lack of "power" in the temperature anisotropies on large angular scales.

What that sentence means is that when you look at the CMB in very large patches on the sky (about the size of the moon and bigger) its temperature fluctuates from patch to patch less than we would expect.

This was already somewhat the case before the BICEP2 discovery, but BICEP2 made it much more significant. The reason for this will hopefully turn into a post of its own one day, but, essentially, the primordial gravitational waves that BICEP2 has hopefully discovered would themselves have seeded temperature anisotropies on these large angular scales. Previously, we could just assume that the primordial gravitational waves had a really small amplitude and thus didn't affect the temperature much at all. Now, however, it seems like they might be quite large and therefore, this apparent lack of power becomes much more pertinent.

That's all fine and is something that any model of inflation that hopes to explain the origin of these gravitational waves will need to explain, despite what many cosmologists already writing papers on the ArXiv seem to want to believe (links withheld). As a side, ever-so-slightly-frustrated, note, the only papers I've seen that have actually analysed the data, rather than repeating old claims, have confirmed this problem that was clear from, at the latest, the day after the announcement.

But why does it imply a "cosmological coincidence problem"? And why is it a new coincidence problem? What's the old one?

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?

Twitter: @just_shaun

On inflation and the multiverse

[Note: in the following, and in the title, I have used the word multiverse a lot. When I do I am exclusively referring to this type of multiverse, which has, for example, been used to try to explain why the cosmological constant it so small. If you have any questions then please do ask them.]

About a week ago, Peter Coles, another cosmology blogger (who also happens to be my boss' boss' boss - or something), wrote a post expressing confusion about the association of inflation with the multiverse. His post was a reaction to a copy of a set of lectures posted on the arXiv by Alan Guth, one of the inventors of inflation (and discoverer of the name). Guth's lectures claimed, in title and abstract, that there is a very obvious link between inflation and a multiverse. Peter had some strong comments to make about this, including the assertion that at some points he's inclined to believe that any association between inflation and a multiverse is no different to a thought pattern of: quantum physics ---> woo ---> a multiverse!

I have some sympathy for Peter's frustration when people over-sell their articles/papers, and I would agree that inflation does not require a multiverse to exist, nor does inflation itself necessarily make a multiverse seem particularly likely/obvious. However, it is also true that, in a certain context, inflation and a multiverse are related. Put simply, through "eternal inflation", inflation provides a mechanism to create many Big Bangs. To get the sort of multiverse this post is about, these different Big Bangs need to have different laws of physics, which is not generic. However it can occur if the laws of physics depend on how inflation ends, in a way which I will describe below.

As with Peter though, I am unaware of any complete inflationary model that will generate a multiverse. We could both have a blindspot on this, but my understanding is that the situation is that people expect (or hope?) that complete models of inflation derived from string theory are likely to generate a multiverse for reasons that I will describe below.

Before that, you're probably wondering what this inflation thing is...

Inflation

The inflationary epoch is a (proposed - although the evidence for it is reasonably convincing) period in the past where the energy density of the universe was almost exactly constant and homogeneous (i.e. the same everywhere) and the expansion of the universe was accelerating. After this inflationary epoch ended, the expansion was decelerating (which isn't surprising given that gravity is normally attractive) and the universe gradually became less and less homogeneous, until it looked like it does today. We like inflation for all sorts of reasons, but for the purpose of this post, the preceding two sentences are all you need to know.

This is the "potential energy density" stored by a hypothetical inflationary field, \(\phi\). The x-axis is the value of \(\phi\). The y-axis is the energy density. The hatched region is where the conditions for "eternal inflation" would be satisfied.