Cosmological perturbations post-Planck - wrap up

Helsinki at midnight. OK, that's not Helsinki, and the photo wasn't taken at midnight. But it is in Finland (Kemiö) and was taken after 11:30pm. Image credit either Chris Byrnes or Michaela D'Onofrio, I'm not sure, although because I got it off facebook, I guess it belongs to Mark Zuckerberg now.

I'm very sorry. As I wrote last week, we just hosted a conference here in Helsinki. I wanted to cover it as the conference happened and I just didn't have the combination of time and mental energy to do so. I won't be covering it in any detail retrospectively either because I need to get on with research. Nevertheless, this blog is slightly more than a hobby for me, it is also slightly ideological, so I will try to work out how to do it all better next time and try again then (this will be the annual theoretical cosmology conference "COSMO" in early September).

Here's a summary of some of the more interesting aspects that I'll quickly write up, starting with some closure concerning the topic I was halfway through in my last post...

David Lyth, the curvaton and the power asymmetry

David Lyth receiving the Hoyle Medal. David's the one in the photo who doesn't already have two medals. From this photo it seems that the guy on the left is graciously donating one of his many medals to David. I got this image from Lancaster University.

Where I left my last post I was describing David Lyth's talk about explaining the possible asymmetry in the amplitude of fluctuations on the sky (as seen through the temperature of the CMB). It's a small effect, the sky is almost symmetric; but it could be a real effect, the sky might be slightly asymmetric.

The possible asymmetry was seen before Planck and one candidate explanation involves quite large super-horizon fluctuations in some of the properties of the universe. "Super-horizon" here means fluctuations whose characteristic scale is bigger than the currently observable universe, i.e they are outside of our observable horizon. Such a fluctuation would be seen by us, within the observable universe as a smooth gradient in the fluctuating observable. Put simply, the idea is to have a smooth gradient in the amplitude of the measured temperature anisotropies. This would quite naturally result in a bigger amplitude in one direction, than another.

It seems that simple inflation can't achieve this without making the fluctuations in the universe significantly non-Gaussian. However, the curvaton can do it (according to David and a paper he is working on). Quite nicely, there is a relationship that David discussed that occurs between the amplitude of the asymmetry and the amount of deviation from a Gaussian distribution one would expect in both an inflation model and a curvaton model. For inflation, the deviation is too big, but for the curvaton it is small but not insignificant. This is nice because, according to David, if this asymmetry is real and the curvaton is responsible for it, then the fluctuations will be measurably non-Gaussian.

This means we can either rule this mechanism out as the cause of the apparent asymmetry, or even better, get evidence supporting it and thus supporting both the curvaton model and the real-ness of the asymmetry. So, watch this space...

Topological defects

Martin Kunz (source). Martin is wearing a hat that almost looks like a Mexican Hat. Mexican Hat potentials are well known sources of topological defects. Imagine a ball rolling off the very top of Martin's hat. It could roll in many different directions. Now imagine that in some parts of the universe it rolls one way, and very far away it rolls another way. A topological defect has formed.

There were a few talks about things called topological defects. The name sounds fancy, but these things are actually, sort of, quite mundane. At least that was what Martin Kunz said in his talk and he had a good point. At least, he convinced me.

"Topological defects" are everywhere. They're basically imperfections in a state of matter. The classic example of a toplogical defect occurs in a magnet. If you heat many magnets up to a very high temperature they will lose their magnetism. This is because all of the individual dipoles (these are basically tiny microscopic North-South magnets) within the metal will have enough energy to overcome the attraction they feel between each other. Just as if you get two magnets and hold them together they will align themselves North-South-North-South, so do the dipoles within a magnet if they're cool enough. Get them hot enough and they'll point in random directions (because of thermal energy) and the over-all substance will have no magnetism. However, if you then cool the magnet again the dipoles in different regions of the magnet will cool with different alignments. This would be a topological defect. At some point in this substance, the two different alignments will meet and you'll either get a South pole next to a South pole or a North pole next to a North pole.

And, as everyone knows, like poles repel. So, this is an unfavourable state for the magnet to be in, thus it is a topological defect. Topological because it is some configuration of the magnet as a whole and defect because it isn't the most favourable, lowest energy state.

Every time a substance undergoes a phase transition (e.g. from unmagnetised to magnetised, from liquid to solid, from plasma to neutral fluid) there is the potential for topological defects to occur.

The universe started out in a very hot and dense state, whereas now it is very cold and sparse. Therefore, it is natural to expect that the universe went through many phase transitions throughout its history. In fact, it did. We know of some of them. The formation of the CMB is one, when the universe went from a charged hydrogen plasma to neutral hydrogen. Another is when quark's and gluons condensed into protons and other nuclei. During each of the known phase transitions (and more interestingly, during any that we might not know of) topological defects could have formed. In fact, Martin went as far as saying they will have formed. And he's right.

But how can we see the effects of them?

This is where things get a bit sad for those who work on topological defects. Unless the defects store a lot of energy (remember the magnetism defect, the two South poles facing each other store energy because they would release energy if the magnet returned to its more favourable state of North-South-North-South) it is quite tricky to see them. The hope was that topological defects might have formed at very high energies, in which case we could have seen their effects on the CMB. In fact, before the acoustic structure of the fluctuations in the CMB was seen it was possible that the fluctuations in the CMB were formed entirely from topological defects. However, as we all know Planck saw a CMB that was consistent with no new interesting things like topological defects.

So, again, we're stuck in a position where there is a well motivated thing to look for, but no evidence of it yet. Perhaps with topological defects the situation is better than with things like the curvaton. At least, this is what Martin convinced me of in his talk. It is almost certain that topological defects did form in the universe's history, the question is only whether they will ever be observable.

Topological defects and gravitational waves

Dani Figueroa, in action at the conference. Source, Mark Zuckerberg.

Which leads me to quite a troubling talk, by former Helsinki postdoc, now Geneva-based, Dani Figueroa. The talk itself was very good and the physics he discussed was top notch, its just the result that is troubling (well, not really troubling... just read on). Dani gave a really nice blackboard talk (without notes I should add, which suggests he either has a really good memory or he's given this talk a number of times). I really can't claim I followed the whole thing, he only had 30 minutes and topological defects aren't something I've ever worked on;

However, his topic was the gravitational wave signal expected from certain types of topological defects (there are many types of defect depending on how dimensions they form in - i.e. whether they look like points, lines or planes in space... imagine cracks in glass they could either be isolated at a point, or a thin line on the surface, or a whole slice through the glass - and whether they have a directional dependence or not - this is a bit more tricky to explain, so I won't unless asked). It turns out that some types of defect produce a gravitational wave signal that is scale invariant. Technically, Dani even proved this in his talk. However, he was going kind of fast and all I remember is that the right hand side of his equation, which initially depended on scale, after a few lines of rapid working, suddenly didn't (all the \(k\)'s in his integral just kind of cancelled).

Anyway, why is that such a big deal? Well, those who are rabid fans of The Trenches of Discovery might remember my post about the implications of Planck for inflation. In that post I claimed that a scale invariant amplitude of gravitational waves would be smoking gun evidence for inflation. If Dani and collaborator's results are true, this kind of throws the cat amongst the pigeons regarding that.

Such is life though, I guess.

"The big splat"

A commenter (masodo) asked me a question during the conference about something called "the big splat". Now I have to admit that I'd never heard of "the big splat" before he or she asked this question, but google tells me that it is another name for the "ekpyrotic/cyclic" universe, which I definitely have heard of (I think the "big splat" name is before my time).

Masodo wished to know what the implications were from Planck for the big splat and whether it was discussed at the conference.

Firstly, the ekpyrotic universe is a replacement for inflation, but not the big bang. In the ekpyrotic scenario the fluctuations in the universe's density, etc are created during a contraction phase, but then the ordinary big bang still happens after that. Nobody in cosmology doesn't believe in the big bang any more (sorry for the double negative). Nobody. Even the people who used to work on steady-state models now work on oscillating models that are "steady-state" (i.e. periodic) in the long, long, long term. The temperature and polarisation of the CMB has within it evidence of sound waves that were rippling through the universe 14 billion years ago when the universe was ~1000 times hotter than it is now and they look exactly like the big bang predicted they would decades ago. We will definitely gain new understanding into how the big bang happened, what started it, what came before it, etc, etc, but it did happen!

Regarding the "big splat" it wasn't discussed during the conference in a scientific context. Not too many people work on it. If one of those people had been at the conference I'm sure it would have been discussed, but none were. It was discussed a little bit at the coffee breaks but only because Hiranya Peiris (one of the conference guests) was having a public debate with Paul Steinhardt (one of the creators of the ekpyrotic model) over skype and she was canvassing people's thoughts.

The people who work on the ekpyrotic universe (e.g. Steinhardt) have claimed that Planck shows evidence that favours this scenario over inflation. This is not the consensus.

Moreover, both paradigms have issues. Inflation has a problem with initial conditions; that is, the universe has to be in a specific state in order for inflation to begin. It's hard to quantify what a "generic initial universe" should look like so most cosmologists don't worry about this problem. Once that problem is ignored there do exist complete models of inflation that can take us from an inflating universe all the way to today. The ekpyrotic universe is less well developed, but its major problem is that it requires the universe to go from a contracting phase to an expanding phase. I haven't studied the model in detail and the creators of the model have speculative ways for how this could happen, but it does make the paradigm less compelling. Note that there is a qualitative difference in that, once inflation has started, it does work, but this change from contracting to expanding has to happen after the fluctuations in the universe have been generated, so it is a more pertinent problem for the ekpyrotic universe than the initial condition problem is for inflation.

Given this, until evidence does arrive that favours the ekpyrotic universe over inflation the "most probable" paradigm is inflation (at least according to my priors). However, until evidence arrives that overwhelmingly favours inflation, research into alternative paradigms is definitely still worthwhile. No matter how compelling we find it, inflation might just turn out not to be true.

Thanks masodo for the great question!

Fire away if you have any more!!

Sorry, that's it

That's it from the conference for me though. If anybody has any questions feel free to ask them in the comments. I have some ideas for how to do this better next time. You live and learn...

Twitter: @just_shaun