Sunday, March 24, 2013

Planck: All we need is six numbers to describe the universe

As I'm sure most of the readers of this blog are aware, the Planck data is now out. It turns out I was correct with two out of three of my rumours. I said that the "ISW mystery" was still present, it was. I said that Planck would present ~3\(\sigma\) evidence for non-zero neutrino masses, they did (though, as I suggested in my rumour, only after including information from galaxy clusters Planck has detected). Finally, I said that there would be 2-3\(\sigma\) evidence for some type of "non-Gaussianity", there wasn't. I will duly update my should-I-trust-that-rumour? algorithm in the following way: explicit remarks from Planck members, good rumour; wishful thinking from other theorists, bad rumour.

So what were those results? What big news is there?

The answer is that there isn't anything strikingly new or surprising. I've been trained by years as a theoretical physicist to to dread that sentence and, indeed, many of my colleagues have gone into various states of despair. But, for some reason, I spent the second half of last week in a state of excited wonder. Surprisingly, I loved what I saw on Thursday. It was both stunning and beautiful. This post will be me trying to explain why. (For more details of the actual results see Sesh's post and Peter Woit's list of other blog posts).

The model of cosmology that has been gaining traction over the last decade and a bit is called \(\Lambda\)CDM. This stands for \(\Lambda\) Cold Dark Matter, where the \(\Lambda\) represents the poorly named "dark energy". This model has a few theoretical issues, but it is incredibly simple. What Planck specifically found is that this model fits the CMB (Cosmic Microwave Background) very well and better than any alternative that they tested.

Why I found what Planck saw to be incredible

As I wrote above, Planck's results last Thursday had me in a state of impressed awe. On the day, I couldn't quite put my finger on why, until I read another cosmologist's tweets marvelling at how everything we were seeing could be described by just six parameters. Then it hit me. For once, cosmology had gotten it right. What Planck measured depends on a significant variety of physical phenomena. If the early universe had more matter, or more radiation than we expected, Planck would have seen it. If the primordial density perturbations had been shaped in a significantly different way to that in which we expected, Planck would have seen it.

Cosmology gets a lot of flak from some directions for the so-called "epicycles" of dark matter and dark energy. I can kind of understand this when people see images like this and are told that we "don't understand" 95% of the energy density of the universe. But what is often missed is that we include the effects of dark matter and dark energy in this \(\Lambda\)CDM model with one, single, parameter each. And once those parameters are fixed, the predictions of all of cosmology are too.

With this firmly in mind, take a look at Planck's most important, headline image below. This (sort of) shows the amplitude of the temperature fluctuations in the CMB as a function of their angular scale. Remember, it takes just six numbers to define what that entire curve should look like. Just six.

The red bits are the measured data, the green curve is the best fit model. The line only needs six parameters to describe it and it just goes straight through the data. Somehow, a crazy species of ape that spends half its time trying to kill itself has managed to both predict this curve so accurately and then put a satellite in space, cool this satellite so that it is colder than space and measure the curve. Awesome.

Anyone who isn't a fan of dark matter and dark energy should take a moment and think about the following: Only one of those six parameters was included in the cosmological model in order to explain an aspect of the temperature fluctuations in the CMB. However, each and every one of them will affect the CMB in non-trivial ways that Planck can see. And finally, everything that Planck saw can be described by this model.

Here are the six parameters (in one particular parameterisation) and why we first needed them in cosmology.

  • The Hubble parameter: The Hubble parameter describes the expansion rate of the current universe. We've needed a Hubble parameter since Hubble first noticed the expansion of the universe. This was at the beginning of the 20th century, long before the Big Bang model even existed, let alone measurements of the CMB or its anisotropies.
  • The density of dark matter today: Dark matter also pre-dates the Big Bang and the CMB. It was first postulated to explain why galaxies were rotating too fast
  • The density of dark energy: "Dark energy" has been required by modern models of cosmology because the expansion of the universe appears to be accelerating today.
  • The amplitude of the primordial density fluctuations: There are galaxies in the universe. Therefore, there needed to be very small fluctuations in the density of the very early universe, around which these galaxies could form. Precisely how big these fluctuations were, is a free parameter.
  • The spectral index of the primordial density fluctuations: The amplitude of these density fluctuations could depend on their physical size. Fluctuations in the density could be more pronounced on small distance scales, or on long distance scales. Note that this is the one parameter that could be argued to be required as a consequence of the CMB

  • The optical depth due to reionisation: After stars form, they emit enough energy to partially ionise the neutral hydrogen remaining in the universe. By the time this happens, the hydrogen is very diffuse and therefore the universe does not become opaque again. However, the CMB will sometimes scatter of the released ions. The "optical depth" measures how far back in time this reionisation process occurred. While the optical depth is not a fundamental cosmological parameter, we don't understand the reionisation process well enough yet to remove it from the model. Once this one parameter is fixed though, we have no more freedom to play with.

And that's all the freedom there is in the simplest cosmological model. Fix those 5+1 numbers and everything the CMB could show us is fully predicted by the model. If we know the constituents of the universe today and how fast it is expanding, we can run the clock back and work out what the universe looked like when the CMB formed.

There was no guarantee that the real world would follow suit and produce a CMB that matched this prediction, but it did. The fact that we only need those 5+1 numbers to describe such a rich range of cosmological phenomena is itself surprising and I happen to find that remarkable.

One curious observation

The greatest mystery in modern cosmology is what "dark energy" actually is. Planck was never going to shed much light on this because the CMB is a probe of the early universe, whereas dark energy primarily affects the late universe. In fact, Planck on its own does not constrain the nature of dark energy strongly at all. It is curious to note that both of the anomalies I mentioned at the beginning of this post (the ISW mystery and the under-abundance of galaxy clusters) relate not to the primordial CMB, but to how local structures have affected it. If dark energy were not the simple constant our model assumes it to be then it is much more likely to show up in these probes than any other aspect of CMB physics.

Where to now?

Next week I will be attending the scientific conference related to Planck's release. There will be many talks given by Planck scientists and many by scientists outside of Planck. I am going to try my absolute best to write a post each day, summarising what I found interesting and what I learned from that day's talks. This won't be an easy task I'm sure, but it is also partially for my own benefit. Forcing myself to write coherent blog posts on the day's talks will force me to concentrate and think about them during the day. Also, if I am confused by something I can write it here and hopefully someone will answer. Finally, if I have any misconceptions, hopefully I will write them down here and have somebody call me out on them, allowing me (and every reader) to learn the truth.

If any readers are interested in any particular talk or Planck-related subject, let me know in the comments or on twitter and I will try to pay particular attention to that talk.

At the end of the conference, I will write a summary of what we've learned from Planck and speculating on where cosmology will head to next. Reader's thoughts (both now and during the conference next week) will be very welcome.

Twitter: @just_shaun


  1. Hi, I just recently started reading your blog -- love it! Can you direct me to the paper in the Planck Legacy Archive that confirms that the ISW mystery is still present?

    1. Thanks! And sure, no problem. It is paper XIX (in particular, section 5). The arXiv link is here:

      Figure 7 of that paper is the relevant one for the original measurement by Granett et al.

  2. Thank you very much Dr.Shaun.
    I would be grateful if you shed light on inflation models after Planck and especially Hybrid inflation and its extensions.

    1. Thanks for the question (and please, just call me Shaun!).

      If you stick around, hopefully exactly this sort of question will come up a lot next week at the conference in Noordiwjk (it looks like the inflation talks will come on Thursday). So hopefully I get to address it in detail then. If I don't, please ask the question again.

      I'll give you a brief answer now though. The original, hybrid inflation model was ruled out when the spectral index was seen to be red tilted, rather than blue tilted (i.e. that the amplitude of primordial fluctuations is greater on large scales than on small scales). However, nowadays, "hybrid inflation" has come to mean any inflationary model that ends via a hybrid transition (a hybrid transition here means a second field becomes unstable when the inflaton reaches a particular value and suddenly causes the end of inflation). Using this definition of "hybrid inflation" there will be many models that have survived Planck.

      Your question is a nice one though, so even if I do write some brief points about inflation models next week, I might try to tackle the problem with another, more detailed, post after the conference (or find an appropriate guest poster).

      I hope that helps...

    2. Thanks a lot Shaun. Have a nice time.

  3. "The model of cosmology that has been gaining traction over the last decade and a bit is called ΛCDM. This stands for Λ Cold Dark Matter, where the Λ represents the poorly named "dark energy"."

    Noo... I write this as interested in astrobiology. (And boy, do the standard cosmology help, with definite age, structure evolution and basis for chemical evolution, and what not.) I'm just trying to unconfuse terminology for us borders:

    This is fluid, but Planck should congeal it: DE and DM should stand for the observational properties or entities as we now know them. When we get to the now well tested 5+1 parameter model they turn out to be some cold DM (CDM) and a cosmological constant (Lambda). (After looking at '100s of millions of models' in some cases I think the ESA press conference said, with DE & DM of various kinds.)

    (And at the current time I take it the "cold" DM is well constrained. But time and other possible variation of the presumed CC is still somewhat open, so DE will be an observational term for the time being.)

    And thanks for the intended coverage!

    1. Hi Torbjörn, thanks for the comment.

      I have to admit, I'm not entirely sure I understand what your intended point was. I called \(\Lambda\) (i.e. dark energy) "poorly named" because it isn't really "dark" at all. That word implies something to do with light and dark energy, whatever it is, has nothing to do with light at all.

      I also happen to think dark matter is poorly named. The much better name would be transparent matter.

      Dark just sounds more mysterious and exciting, so the names have caught on.