Monday, April 8, 2013

The universe as seen by Planck - Days Three and Four I

Sorry for the delay on this. I was pretty tired on Friday, travelling home on Saturday and doing physics on Sunday. I figured it would be better to write something with a little more care today.

Those who were following last week will know that on March 21 ESA finally released some cosmological results from the measurements they were taking with the Planck satellite. And, last week, they had their first scientific conference. I decided to blog about this. I had the initial ambition of one post for each day, but the conference dinner on Thursday beat me and all I got out was a brief teaser post. This post now will be comprised of a summary of what I found interesting on both Thursday and Friday, along with a summary of the whole conference at the end.

I hope you enjoy it (and thanks for the feedback during the week).


  • What has Planck told us about inflation?
  • What should we make of Planck vs SPT and Planck vs the local universe?
  • What is next for CMB science?
  • Some final thoughts

What has Planck told us about inflation?

Slava Mukhanov. Cosmology can do what it wants, but Mukhanov's  predictions for inflation will remain unchanged. Somehow cosmology always seems to come back to him in the end. Will that last missing piece show up? Will primordial gravitational waves one day be detected? It's starting to look like a "no", but Mukhanov's heard that talk before. Time will tell...

The first talk on Thursday was about inflation, by another one of the scientists who helped found it. This was by Slava Mukhanov, another old-school Russian physicist. Mukhanov was one of the first to realise that inflation wouldn't just cause the universe to expand dramatically and to make it more homogeneous, it would also seed new fluctuations with a very small amplitude. These new, small, fluctuations arise from the stretching (and eventual amplification) of quantum fluctuations in the field driving inflation. This type of realisation was what took inflation from an interesting concept to a testable paradigm.

With satellites like Planck those perturbations are now being ever more precisely examined.

Mukhanov has a very different perspective to Linde regarding what inflation can or cannot explain. To him the question of whether a theory is scientific or not comes down to one thing and one thing only: has it made unique a priori predictions that can then either be verified or used to rule out the theory? From that perspective his view is that inflation has only ever predicted one set of results and those are the predictions of the first, simplest models of inflation. He makes no distinction as to whether those models are well described by a quantum field theory model or not.

I don't happen to agree with this perspective and I don't think most practising physicists would either. Inflation might be true and yet not described by one of those original models. If that is the reality, then I would want science to be able to test this reality.

However, Muhkanov deserves credit for at the very least sticking religiously to his guns. He likes to show slides during talks like this that were written on overhead transparencies in the early 90's. This dates these slides to an era before the anisotropies in the CMB were discovered, before the late-time accelerated expansion was discovered and a time when the total observed mass in the universe was indicating that the curvature in the universe might be significant (i.e. in technical terms it would be "open"). These slides make a number of specific predictions for what inflation requires (by Mukhanov's definition of inflation).

  • A flat universe (i.e. no curvature)
  • Perturbations that had a Gaussian distribution
  • Perturbations that were almost scale-invariant, but not quite (they would need to have a slightly larger amplitude at larger scales)
  • Perturbations that were adiabatic (i.e. all the constituents of the universe were perturbed in the same way)
  • A small, but not insignificant quantity of primordial gravitational waves

How many of these predictions have now been verified?

All but one.

The reason why Mukhanov deserves credit is that at two separate points in history at least one of these predictions has been in serious jeopardy. I mentioned above that when Mukhanov was first writing these predictions down, there seemed to be some evidence that the universe was open. At that time, some inflationary theorists (Linde amongst them) were trying to construct models of inflation that could generate an open universe. Mukhanov said in his talk that at this point of history he was considering leaving cosmology because he believed inflation could not survive as a predictive science if the universe was open. It turned out that those tentative hints of open-ness were actually the first evidence of the consequences of the accelerated expansion and that the universe is flat.

Then, last decade the WMAP satellite was showing not insignificant evidence for a large degree of "non-Gaussianity" in the CMB. If that had been verified, Linde's inflation would have survived (after all it can explain anything), but Mukhanov would have pronounced inflation dead. Planck showed that WMAP's evidence was only a statistical fluctuation and that, to Planck's accuracy, there is no evidence for primordial non-Gaussianity.

Mukhnov's view of inflation seems to be surviving quite well.

There is that one missing piece though.

These are primordial gravitational waves.

Can we ever prove inflation right or wrong?

If you will stick with me I am about to explain how it is possible that Planck's observations have simultaneously made it more likely that inflation is correct but more difficult to ever prove it right beyond doubt. I appreciate that this sounds a bit silly, but read on.

If you look at the list of predictions from Mukhanov's inflation one thing that might leap out at you is that most of the predictions are basically the absence of something (except the primordial gravitational waves, but I'll get to them). No deviations from Gaussianity (which is the default because of the central limit theorem). No curvature. The perturbations in each field are the same. The fact that each of these predictions has occurred definitely strengthens the case for inflation, but it doesn't prove it beyond doubt, because each prediction is also kind of the default.

Compare this to the Big Bang. We know the Big Bang occurred because it made a collection of very non-trivial predictions (e.g. the existence of the CMB and the fact that its temperature and polarisation would be correlated and would carry the evidence of primordial sound waves, etc). What inflation needs is to also have something non-trivial.

What many theorists were hoping for is that inflation was correct, but that it was Linde's view of inflation that was correct, not Mukhanov's. In this case, there could have been some non-Gaussianity, or some other feature. Through the analysis of these features, a distinctive signature of one of the many other models of inflation might be seen. We might rule out the simplest model of inflation, but the hope was that we would detect a more complicated (perhaps even less compelling) alternative model. The fact that any features that might exist have so far evaded our detection makes this possibility less likely.

Hence, the case for inflation has improved from Planck (i.e. the predictions of its simplest models and its most compelling models were verified), but the possibility we might one day verify it beyond doubt has decreased (i.e. the most compelling models make rather neutral predictions, without distinctive features).

A future colleague of mine, Chris Byrnes (thanks for the job dude!) showed this comic in his talk. Chris (like me) is a theorist who has worked  on models of inflation that can generate non-Gaussian primordial density perturbations. The comic pre-dates Planck, but I think it explains what Planck did to these models quite well. These more exotic models could still be true, but the exotic parts of them seem to have "no influence on the Universe whatsoever". Nature can be cruel.

The are two non-trivial predictions in Mukhanov's list. I'll still get to primordial gravitational waves, but the other prediction is the almostness for the scale invariance of the primordial curvature perturbations. If inflation predicted pure scale invariance and that had been observed, it would be as bland and as neutral as flatness, adiabaticity or Gaussianity, but it didn't. It predict almostness for the scale invariance. Planck has now verified, that in the \(\Lambda\) CDM model, the primordial perturbations are not scale invariant and that they deviate from scale invariance by just the right magnitude to match Mukhanov's prediction. This was non-trivial, but it is just one number. Maybe that one number coming out right was a fluke? Compared to the entire curves I showed you last week that match what we expect from primordial sound waves and thus provide irrefutable evidence for the Big Bang, getting one number right isn't quite enough to convincingly determine that inflation really did happen.

It's definitely a murder weapon, found at the scene of the crime, but it isn't a smoking gun.

So, is there a smoking gun for the simplest models of inflation?

Does inflation have a smoking gun?

And now I get to primordial gravitational waves, the only piece missing from Mukhanov's puzzle and what, if they were detected, would surely warrant, for Mukhanov, one of the most well deserved utterances of "I told you!" in the history of humanity's pursuit of knowledge. He would have spent more than twenty years, resolutely saying the same thing over and over again, while the rest of the community flitted backwards and forwards, only for them to eventually settle down exactly where he has stood, unmoved, from the beginning.

(Almost) Every single model of inflation predicts that there would exist primordial gravitational waves that are also almost scale invariant. This level of prediction is at last non-trivial. The existence of almost-scale-invariant primordial gravitational waves would indicate that, early in the history of the universe, the energy density of the universe was very large (to generate the waves) and almost constant throughout space and time (to make sure they are scale invariant). This is very nearly the actual definition of what is required to generate an inflationary epoch.

The big problem is that the amplitude of these waves depends on the model. For some models (the simplest) the characteristic effects that these waves would have on the CMB's polarisation are right on the verge of detection by Planck. For others (arguably the most compelling) they are so small that we'll never see evidence of them.

Sadly, we are starting to reach the point where Mukhanov's brand of simple inflation is going to be ruled out (I guess Mukhanov would say that he's heard this kind of statement a few times before). It still survives, but barely. If it does get ruled out, but inflation is still true, then these primordial gravitational waves will be there. But, there is no reason to expect that they will be loud enough for us to ever detect them. Maybe inflation occurred at a low enough energy scale that we'll never see the primordial gravitational waves it inevitably generated, but at a high enough energy scale that we'll never be able to probe inflationary physics with a collider. The window between those two energy scales is enormous.

This might leave us, for many generations, in the awkward position that inflation seems compelling and likely, but still hasn't quite been verified beyond doubt. But such is life for an observational, rather than experimental, science. We can only observe what nature has chosen to make observable.

If we assume inflation is true, have we learned anything about it?

I wrote above that Mukhanov's favoured simple brand of inflation and the other (arguably) most compelling models of inflation make rather neutral predictions. I also said that there were other models that made less neutral predictions. So surely, at the very least, if we assume inflation is correct, the observations of Planck have said something about inflation, even if it is just that those other models were wrong?

Correct (mostly)!

If we assume that inflation is true then Planck's observations are starting to say some kind of interesting things about what type of inflation might have generated our Big Bang. In a talk on Thursday Mattias Zaldarriaga gave a nice talk about what Planck has told us about inflation. He made some nice observations.

We know inflation must end and that the inflaton must end up in a stable vacuum state (or inflation would still be happening and we wouldn't be here now). In the language of a Taylor expansion, the first term around this vacuum would be \(\phi^2\). Now, Planck is on the verge of ruling out \(m^2\phi^2\) inflation. If \(m^2\phi^2\) inflation is ruled out, then we can say, using a kind of Taylor expansion measure of the distance from the vacuum, that during inflation the inflaton field was far from the vacuum. Or, in other words, at least one other term must exist in the inflaton's potential!

I find that kind of neat. There isn't enough information to determine what that term is, but we know it must be there. That would be one non-zero piece of information about the particle content of the early universe that cosmological measurements have now provided us with. No collider will ever probe those energies, but, through cosmology, we have gained at least some information.

We will soon know a little bit more. If Planck does not verify the existence of primordial gravitational waves, then as you can see from the figure below, this would eventually require the potential of single field inflation models to be concave during inflation. The minimum we lie in now must be convex. Therefore, we know that at some field value the curvature of the inflaton potential must change. Again, this isn't a substantial fact, but it is a fact, a fact about the particle content of the universe at incredibly high energies.

This shows the amplitude of primordial gravitational waves (y-axis) vs how far from scale invariant the primordial curvature perturbations were (x-axis - 1.00 would be scale invariant). The blue contours show the space allowed by Planck. The black dots show \(m^2\phi^2\) inflation, the simplest model of them all. I must have spent a solid six months in the first year of my doctorate staring at WMAP's version of this figure each day, mostly confused, trying to reproduce someone else's unreproducable work, and not really making much progress. Good times. 
The final pieces of information we have gained relate to these non-observations of features. It was well known before Planck that any slowly rolling, single field, model of inflation could not generate observable primordial non-Gaussiniaty. This is one of the reasons many theorists were so hopeful for a detection of non-Gaussianity, because it would definitively tell us that there was something non-trivial about the early universe. The converse of this is not quite true, multiple field models of inflation can exist without generating non-Gaussianity. However there are reasonably generic things one can still say.

If one were to write down the physics describing the inflaton and parameterise the deviations from the simplest single-field slow-roll situation with a variable speed of sound and/or modified dispersion relation (a modified dispersion relation kind of describes how fluctuations of different scales act within the universe - a "modified" dispersion relation implies the physics is different for different wavelengths) then one would inevitably generate non-Gaussianity. Therefore, the fact that no non-Gaussianity has been observed tells us non-trivial things about the speed of sound and dispersion relation during inflation. There may very well be more than one field, or various other modifications, but those extra fields can't change those quantities.

That's also kind of neat. A measurement that a certain parameter is consistent with zero is still a measurement of that parameter and it does still tell us something about the nature of the very early universe. Whatever its constituents were, the speed of sound in the very early universe was very close to the speed of light.

The one caveat is that for any of those points to become facts does require the assumption that inflation definitely did occur.

Why aren't the simplest models the most compelling?

Physicists and non-physicists might have been puzzled by a distinction that crept into my language above. I separated the simplest models from the arguably most compelling. I added the word "arguably" because I don't think Muhkanov would make this distinction and neither would some others. However I am someone who would. Let me give you the argument why.

(In most models) Inflation empties the universe out of everything except the inflaton. That was actually why inflation was invented in the first place. But, when we look at the universe today it definitely isn't empty of everything except one field. We see hydrogen and lithium and helium and ever more complicated atoms and molecules. If inflation is true and inflation empties the universe of everything except the inflaton field, then, well, clearly everything we see now must have come from the inflaton.

This means that the inflaton field must interact with us. The interaction might be very weak (in fact it has to be) and it might even be indirect through interactions with other intermediate fields, but sooner or later the energy in the inflaton field must turn into the energy in hydrogen, helium, the CMB, etc.

This point was raised by Anupam Mazumdar late on Thursday and it is a major problem for the simplest models of inflation. For inflation to work, the energy density during inflation must be almost constant (but not quite). For this to happen the inflationary potential energy function must be almost flat (or, more precisely, must have an almost flat part of it). Any interactions with messy standard model particles will act to destroy this flatness.

Finding a potential energy function that is stable to this feature is difficult and the simplest inflationary models simply are not stable to it. This means, that even though one can calculate the predictions for the density perturbations generated by these simple models it is very difficult to work out ways of generating our universe's matter without ruining those predictions, or altering the potential so significantly that inflation would no longer even occur.

From this perspective the most compelling inflationary models are those that are complete. These models can generate both the density perturbations and the matter in the universe. Such models do exist, though they aren't without their own (arguably less severe) issues.

The problem for testing inflation is that these models occur at lower energies than the simplest models and thus the primordial gravitational waves that they generate would never be observable. It is technically possible to write down a complete model of inflation that can generate primordial gravitational waves that Planck will eventually detect, but those models aren't simple, nor are they particularly compelling.

Still, time will tell...

[the non inflation stuff has been continued here...]


  1. I had a question - Why is it claimed that inflation predicts a flat universe ?
    If I understand right, just after inflation the curvature is very close to zero - because the universe becomes much bigger than the visible horizon.
    But afterwards the curvature gets pushed away from zero, so today it can have any value, right ?

    1. Hi Cosmonut, sorry that it took me a while to answer this.

      Your understanding is right. In principle the curvature could have any value today. However, the amount of inflation required to make the curvature of order 1 today is basically the same as the amount of inflation required to make sure the current horizon was in causal contact before inflation. Therefore, if the curvature was close to 1 today, our current horizon would also be close to the edge of our inflationary patch.

      The consequences of that would be that the largest scale fluctuations would not have been damped out significantly by inflation and we would not expect things like the CMB to be the same temperature in opposite directions.

      When inflation was first being constructed we already knew that the CMB was uniform to a certain degree (at least one part in 10^3); therefore (ordinary) inflation would also predict that the curvature was equivalently small.

      Basically, because of the isotropy of the universe on the largest scales we know that inflation persisted for at least a little bit longer than it would need to just to generate our horizon. Therefore, the maximum allowed curvature is smaller than 1, by a factor of 1/e^2N, where N is the number of additional efolds. It doesn't take many efolds to make the curvature very small.

      Also, when many people think "inflation" they think "eternal inflation" (because it can arguably overcome the problem of initial conditions in inflation). Eternal inflation would have many more efolds of inflation than just 60 and a prediction of a perfectly flat universe (with the normal inflationary spectrum of small perturbations).

      But of course there are exceptions. And that was what the industry was in the 90's. If the homogeneity and isotropy was set down in a false vacuum period of inflation, which then tunnelled into a slow-roll type of inflation, you could evade the problems I mentioned at the beginning of this comment. The false vacuum inflation would create an open, isotropic, universe and then if you had just enough slow-roll inflation you could get whatever (open) curvature you wanted today as well as an isotropic universe on large scales.

      I hope that helped.

    2. Thanks, Shaun, that was extremely helpful.
      I just have a small followup question:
      Based on Planck's observations, can we put a lower bound on the size of our inflationary patch today in comparison to the horizon ? For eg, can we say the patch is at least 1000 times bigger than the observable universe, perhaps even more ?

    3. Maybe, kind of.

      The biggest problem would be quantifying what the initial conditions before inflation were like. We can't really "predict" them and without knowing them we can't really know what they would look like if we were to start seeing them.

      Based on the fact that the largest scale fluctuations are ~\(10^{-5}\), I think it would be relatively safe to say that the "inflated patch" would be at least \(10^4\) times bigger than our horizon (because fluctuations shrink proportionally to the scale factor during inflation).

      I'm not 100% confident with that, but it's my best guess. This is also all based on knowledge we've had since COBE's results. The precision from Planck and WMAP doesn't really help if we don't have a good theory for what the pre-inflationary universe would look like.

  2. "Planck showed that WMAP's evidence was only a statistical fluctuation and that, to Planck's accuracy, there is no evidence for primordial non-Gaussianity."

    From the Overview abstract:

    "Planck finds no evidence for non-Gaussian statistics of the CMB anisotropies"

    From Planck paper #23 "Isotropy and statistics":

    "We detect pronounced signatures for both non- Gaussianities and anisotropies........a highly significant detection of both non-Gaussianities and anisotropies in the Planck data, consistent with those obtained previously with WMAP data"

    So which is it?

  3. Perhaps even more relevantly:

    Why are directly contradictory assertions published by the same team on the same question at the same time?

    1. Hi Rick,

      It's an unfortunate use of language from Planck. The non-Gaussianities being described in the two papers are different.

      In the paper specifically on non-Gaussianities, they are dealing with effects motivated by various models of inflation. They find no evidence for those specific types of non-Gaussianity and favour the simpler models of inflation.

      In the isotropy and statistics paper they are looking instead for less well motivated types of effects. Essentially they're just looking to see if the data is anomalous in any unexpected way. When you find something like this it is very difficult to quantify how anomalous it is. When you have enough noisy data, you expect to see some areas where the data doesn't match the model precisely (that's essentially the definition of noise). This is what Planck sees, i.e. some areas where the data doesn't fit the model precisely, but nowhere where it is so significantly wrong that it couldn't possibly be noise.

      They have quantified how unlikely these specific deviations are, but what is harder to quantify is the over-all probability that any type of deviation would be seen, which is definitely larger than the probability of the specific anomalies that were observed.

      What this means is that these unexpected anomalies might point towards something new, but they might just be noise. Anything new that is constructed to explain them would of course need to explain both the anomaly and everything else that the original model predicted. This is very difficult to do for these anomalies.

      I hope that helped in some way, sorry again for the delay.


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