## Wednesday, March 27, 2013

### Explaining Planck by analogy

Explaining physics to the public is hard. Most physicists do a lousy job of conveying a summary of what their research really means and why it is important, without the use of jargon and in terms that can be readily understood. So it is not particularly surprising that occasionally non-experts trying to translate these statements for the benefit of other non-experts come up with misleading headlines such as this, or this.

Just to be clear: Planck has not mapped the universe as it was in the first tiny fraction of a second. (To be fair, most other reports correctly make this distinction, though they differ widely on when inflation is supposed to have occurred.) I think this is an important thing to get right, and I'm going to try to explain why, and what the CMB actually is.

However, I'm going to try to do so with the help of an analogy. This analogy is not my original invention – I heard Simon White use it during the Planck science briefing – but I think it is brilliant, simple to understand and not vastly misleading. So, despite the health warning about analogies above, I'm going to run with it and see how far we get.

Ok, let's start with the cosmic microwave background itself. What are these temperature anisotropies we cosmologists are measuring? I tried to explain this briefly near the start of a previous post. I mentioned there the basic stuff about the hot dense ionised plasma with photons bouncing off electrons, so that the universe is opaque. I then mentioned how the universe cools as it expands, until hydrogen atoms can form out of the plasma and suddenly the universe becomes transparent and the photons travel for billions of years until reaching the Planck detector.

What I realise I didn't mention was what we are actually looking for in the temperatures of these photons. The answer is waves. Sound waves. That's because there were oscillations – sound waves – in the original ionised plasma when the CMB was formed 380,000 years after the Big Bang.

Obviously, it's a big universe, and there are a lot of waves to be seen. Any single wave doesn't convey a lot of information. So imagine that you were looking at a surface with lots of waves on it:

and you were to perform a statistical analysis of the properties of these waves, by calculating the average height of the waves as a function of their length. And then you make a plot of this.

 The CMB power spectrum as measured by Planck. Image from arXiv:1303.5062.

That's what the image above is: the "power spectrum" measured by Planck is in a sense just a measure of the height of the waves in the primordial plasma as a function of their length. [I wish someone had explained this to me when I took my first course in cosmology as an undergraduate – our lecturer spent ages showing us slides of the power spectrum without ever actually telling us what the quantity $\mathcal{D}_\ell$ on the $y$-axis was, nor what the "multipole moment" $\ell$ referred to. The Planck figure helpfully shows how $\ell$ relates to the angular separation of points on the sky.]

Now, instead of the sea as pictured above, imagine that you are seeing these waves on the surface of a cloud. The region between you and the cloud is generally transparent, though there may be large annoying foreground things in the way that obscure your view of the cloud. But if you manage to look past them, or through them, you see light that has travelled to you directly from the cloud surface. Also, the cloud is opaque; you can't see anything behind it, even though you know that there are things there.

The other thing you know is that the cloud is a long way away from you, and that light only travels at a finite speed. So clearly the patterns of waves you see on the cloud are the patterns present a long time ago, when that light set off on its journey towards you.

Now I'm sure this is obvious already, but the analogy I am making is between the cloud and the last scattering surface (here's a completely different analogy you might also like). Like with real clouds, the surface of last scattering is not completely sharply defined: there's a small amount of fuzziness as the universe makes the transition from completely opaque to completely transparent. Some parts of the surface are also very slightly closer to us than others, a property that is connected to the height of the waves we see on them.

It should now be clear that, as this last scattering occurred about 380,000 years after the Big Bang, and the cloud surface is all we can see because the cloud is opaque, and the Planck telescope is actually designed to look at the cloud surface after all, it necessarily sees the universe as it was 380,000 years after the Big Bang, and not $10^{-27}$ seconds after it, contrary to what you may have read elsewhere. Let's come back to this a little later.

First, let's talk about the practicalities of observing this cloud. Unfortunately, there's a lot of stuff in the way that really blocks your view:

 The CMB with lots of foreground. Image credit: Planck science team.

But you find that if you change your spectacles, you see less of the annoying stuff in the foreground and more of the cloud:

 The CMB with slightly less foreground. Image credit: Planck science team.

Also, crucially, the foreground stuff you do see is actually different stuff, depending on which spectacles you are wearing. So by changing between several different pairs of spectacles and performing clever calculations that also involve some assumptions about what it is you expect is getting in your way, you manage to come up with a final picture of what the cloud surface really looks like:

 The CMB with (hopefully) all foreground removed. Image credit: Planck science team.

and you can now start to measure the heights and lengths of waves, and fit your model of what the heights and lengths should look like to what you actually see. Your model includes such things as how far away the cloud is, and how the world between you and the cloud is changing. (For a more technical description of the parameters of the real model, see Shaun's explanation.)

But there's another cool thing you can do. Imagine that you are actually making all these observations indoors, looking out through a window. This isn't a nice modern window, all clear and perfect. Instead it is one of those really ancient windows in which the two sides of the pane of glass are not exactly parallel everywhere and the thickness is not exactly uniform. So the window distorts the image of the cloud you see, changing the patterns slightly depending on which part of the window pane you happen to be looking through.

If you knew how thick the window glass was in each part of the pane, you could exactly correct for this distortion. Unfortunately, the pane is transparent and you can't actually see it, so you don't know its thickness. But – and here's a cool thing! – given your model of what the distribution of heights and lengths of waves should be, which is ever so slightly different to what it is, you can actually your observations of the cloud to determine the varying thickness of your window!

Let's back up a step to make the connection between physics and analogy a little firmer. The window is the matter in the universe that lies between us and the surface of last scattering. It is transparent because most of the matter is actually dark matter, which we cannot directly see. It is of varying thickness because the distribution of matter is not completely uniform – large clusters of galaxies and dark matter halos exist, as well as much more empty void regions. The distortion that this window effects is through gravitational lensing.

 A reconstruction of the lensing potential that slightly distorts the CMB. Image from arXiv:1303.5062.

And finally, let's push the analogy one step further. Let's say your window is actually in need of a wash. You can see some specks of dirt on it, so you know it is there, between you and the far-off cloud. You also think that there are more specks in the regions where the glass is thicker. (Clearly these specks correspond to the visible galaxies embedded within the dark matter structure.) Now you can use these facts to simultaneously test your various models – your model of what the cloud really looks like, and your model of how the window should distort the cloud, and also your model of the distribution of specks on the window. You do this by checking whether the distortions to the image of the cloud that you have inferred are in fact correlated with the positions of the specks you see on the window. If you observe the correlation you expect, you have in fact detected the integrated Sachs-Wolfe effect. (If it doesn't match, you have the tough job of figuring out which of your models is wrong, and why.)

So far, so wonderful. If you previously didn't understand the basic ideas of CMB cosmology with Planck, or even if you did, I hope this analogy helped! But what about the theory of inflation, and the idea that we are directly measuring the universe back to $10^{-27}$ seconds or or $10^{-32}$ seconds or some other ridiculously small number?

Well, what we haven't discussed in this analogy so far is why there should be sound waves in this cloud  in the first place. Ok, maybe I understand the laws of physics as applied to clouds well enough to say that if the cloud started off with some small density fluctuations in it, sound waves would get set up in it, leading to some distribution of heights and lengths for me to measure. (Actually, they probably wouldn't in a real cloud, but play along with the analogy.) But where do those initial small density fluctuations come from?

That's what the theory of inflation is for. You may read various other things about the successes of inflation, such as solving things called the horizon problem, and the flatness problem. I don't think these are particularly convincing. Instead the real reason for the popularity of the theory of inflation is that it provides a plausible mechanism for the generation of the original fluctuations that grow to become sound waves, and that because it provides the mechanism it allows one to calculate through to make quantitative predictions about what these waves should look like (assuming we know everything about the window and the rest of the world between us and the cloud of course!).

Perhaps in the cloud analogy the theory of inflation could correspond to a theory of evaporation of water and the condensation of vapour into droplets or something. In that case, you'd need to add that we don't actually have much concrete knowledge about the evaporation and condensation process and we can't test it in our indoor lab behind the window. So there are lots of speculative bits, and there are many, many different possible variations on our model of cloud formation. These variants don't even agree on when the evaporation and condensation occurred, whether after $10^{-27}$ seconds or somewhat later or earlier. Worse yet, most of these variants end up (by design) making essentially the same predictions for the structure of the cloud, so our actual observations can only rule out a small handful of them.

Let's say the same thing in a different way. We understand the laws of physics well at energy scales below the electroweak scale of around 100 GeV (1 GeV is a giga electron volt, or $10^{9}$ eV). This is the regime in which we have actually tested these laws in particle physics experiments here on Earth. By the time the universe cools enough to reach temperatures associated with this energy scale, the baryon asymmetry should already have been generated by some mechanism as yet unknown. The QCD phase transition then occurs at energy scales of between 100 and 300 MeV (1 MeV is $10^6$ eV), neutrinos decouple from the primordial plasma at around 1 MeV, and the formation of the light elements – helium, deuterium, lithium and so on – occurs at about 0.1 MeV.

The last scattering surface of the CMB is only formed after recombination and decoupling, which occurs at scales of only 0.1 eV – that's energies a million times lower even than those for nucleosynthesis! Remember, it is only at this point, 380,000 years after the Big Bang, that the universe becomes transparent. Planck cannot see anything before this; we can only reconstruct the history of the universe before this point because we know the physics operating up to the electroweak energy scale so well. (We can test nucleosynthesis through cosmology even though it happened earlier than the decoupling because its end products stick around and can be observed in the late universe.)

The difference with inflation is that it is supposed to occur in the energy regime where we don't really know the laws of physics, because we haven't directly tested them in the lab, and we can't directly observe them in the CMB. In fact we don't even really know when inflation occurred: there are 17 orders of magnitude in energy between the the electroweak scale around 100 GeV and the Planck scale at $10^{19}$ GeV, and the restrictions on where in this range inflation could have occurred are not particularly tight. Any ideas about what the universe was doing before inflation are even more speculative!

 A graphical depiction of the history of the universe. Direct observations of events before the era of recombination are not possible. Image credit: Planck.

Maybe you think I'm being a bit pedantic, and that it doesn't matter much if one says Planck is directly observing the inflationary epoch when it isn't, because constraining some generic predictions of inflation models is almost the same thing. I would argue instead that it is vitally important to maintain a distinction between the physics that we know is true and tested by experiment, and the physics that is still rather speculative. And that to do that we need to be more precise in our reporting of it.

1. I've actually been worrying about misleading headlines in my own blog posts this week. To be fair to those people with the headlines about the first trillionth of a second, etc, even the post of mine that you linked to, i.e. "We only need six numbers to describe the universe" title is also very misleading (we actually only need six *additional* parameters to describe cosmology - and even then I'm completely ignoring all parameters involved in modelling foregrounds).

Sometimes you just need to pick a title. As I'm sure you know, this science-writing thing is hard (in many ways its harder to do than the science itself). You want the title to convey something of the meaning of the post, but also to be interesting.

That's not to say I'm not happy you wrote this post. The more information that is there for people to read, the better and it is great that this post now exists to clarify certain points. But those titles are arguably true, as is mine.

There are boundaries that can be crossed where the misleadingness becomes destructive, but I'm not sure where that boundary is myself.

1. It's not simply the wording of the titles of those reports that motivated me. To an extent I think all discussion about what Planck tells us about inflation have been a little over-hyped. These titles were actually factually wrong whereas the wording on the BBC report, for instance, was technically speaking correct. But I felt that even when they avoided outright mistakes, no reporters conveyed a realistic picture of the flexibility of inflationary model-building. That seems to lead to some misconception about what Planck can or will say about inflation, as you can see from the comments on my previous post! And I've even heard similar things from professional physicists, not just members of the public.

Besides, I liked the analogy :)

2. I made an quite an effort not to oversimplify while writing my post, so when I noticed that you'd called me out I thought you were just reading too much into my title. (As Shaun said, sometimes you just need a title...) Looking back over what I wrote, though, I can see that I wasn't clear enough about the difference between what we can actually see & measure (the last scattering 380,000 years after the Big Bang) and what we're just inferring (the density fluctuations during the first second). I didn't realize from my background reading how poorly we understand the early inflation, but your post made it clear. Thanks for setting me straight!

3. "You may read various other things about the successes of inflation, such as solving things called the horizon problem, and the flatness problem. I don't think these are particularly convincing."

Leaving aside the fact that there is no proof that inflation occurred, and also the question whether there is a testable prediction which could in principle rule out inflation, what do you find not convincing? Do you think that inflation does not solve the horizon and flatness problems? Do you think the monopole problem is an issue and, regardless of your answer, why? Or do you think that the flatness and horizon problems do not exist?

Personally, I think the flatness problem in classical cosmology has been overhyped, to say the least (see http://www.astro.multivax.de:8000/helbig/research/publications/info/flatness.html ), but I see no other obvious solution to the horizon problem (or isotropy problem; some people use the term "horizon problem" to mean something different) except for things like variable speed of light, which sounds rather Deus ex machina to me.

On the other hand, while inflation could explain the origin of fluctuations, it seems to me that a Harrison-Zeldovich spectrum could conceivably have some other origin.

1. As far as I am aware, inflation does not actually solve the horizon problem. See for instance arXiv:gr-qc/9811037, from whose abstract I quote:
"In the context of inflationary models with a pre-inflationary stage, in which the Einstein equations are obeyed, the weak energy condition is satisfied, and spacetime topology is trivial, we argue that homogeneity on super-Hubble scales must be assumed as an initial condition."

So the horizon problem exists with inflation too. True, it is possibly a smaller horizon problem, so maybe inflation has helped somewhat. But it is still there.

Many inflationary models have another sort of "initial conditions" problem as well, which is that the scalar field driving inflation needs to start in a particular part of its potential, and the initial conditions may need to be unnaturally fine-tuned to get it in that region. This is in addition to the amount of fine-tuning of the model that may be required to get a potential for the scalar field in which any region is suitable for inflation.

It is quite possible that the initial conditions required to get inflation started are even more unnatural than just starting off with a very unnaturally homogeneous patch as big as our universe (i.e. standard Big Bang with no inflation).

For further reading, you could first have a look at a blog post by Mark Trodden about his paper that I quoted above. He mentions eternal inflation as a possible way out, so you should also read Sean Carroll's description of some of the issues with eternal inflation. (Sean has many more detailed posts about eternal inflation on his blog as well.)

4. Christopher McCabeApril 4, 2013 at 3:50 PM

Hi Sesh. Great post!