# A Tale of Two CMB Measurements

Apparently, researchers have managed to use Planck‘s measurement of the Cosmic Microwave Background to indirectly measure a more obscure phenomenon, the Cosmic Neutrino Background.

The Cosmic Microwave Background, or CMB is often described as the light of the Big Bang, dimmed and spread to the present day. More precisely, it’s the light released from the first time the universe became transparent. When electrons and protons joined to form the first atoms, light no longer spent all its time being absorbed and released by electrical charges, and was free to travel in a mostly-neutral universe.

This means that the CMB is less like a view of the Big Bang, and more like a screen separating us from it. Light and charged particles from before the CMB was formed will never be observable to us, because they would have been absorbed by the early universe. If we want to see beyond this screen, we need something with no electric charge.

That’s where the Cosmic Neutrino Background comes in. Much as the CMB consists of light from the first time the universe became transparent, the CNB consists of neutrinos from the first time the universe was cool enough for them to travel freely. Since this happened a bit before the universe was transparent to light, the CNB gives information about an earlier stage in the universe’s history.

Unfortunately, neutrinos are very difficult to detect, the low-energy ones left over from the CNB even more so. Rather than detecting the CNB directly, it has to be observed through its indirect effects on the CMB, and that’s exactly what these researchers did.

Now does all of this sound just a little bit familiar?

Gravitational waves are also hard to detect, hard enough that we haven’t directly detected any yet. They’re also electrically neutral, so they can also give us information from behind the screen of the CMB, letting us learn about the very early universe. And when the team at BICEP2 purported to measure these primordial gravitational waves indirectly, by measuring the CMB, the press went crazy about it.

This time, though? That Ars Technica article is the most prominent I could find. There’s nothing in major news outlets at all.

I don’t think that this is just a case of people learning from past mistakes. I also don’t think that BICEP2’s results were just that much more interesting: they were making a claim about cosmic inflation rather than just buttressing the standard Big Bang model, but (outside of certain contrarians here at Perimeter) inflation is not actually all that controversial. It really looks like hype is the main difference here, and that’s kind of sad. The difference between a big (premature) announcement that got me to write four distinct posts and an article I almost didn’t notice is just one of how the authors chose to make their work known.

# All Is Dust

Joke stolen from some fellow PI postdocs.

The BICEP2 and Planck experiment teams have released a joint analysis of their data, discovering what many had already suspected: that the evidence for primordial gravitational waves found by BICEP2 can be fully explained by interstellar dust.

For those who haven’t been following the story, BICEP2 is a telescope in Antarctica. Last March, they told the press they had found evidence of primordial gravitational waves, ripples in space-time caused by the exponential expansion of the universe shortly after the Big Bang. Soon after, though, doubts were raised. It appeared that the BICEP2 team hadn’t taken proper account of interstellar dust, and in particular had mis-used some data they scraped from a presentation by larger experiment Planck. After Planck released the correct version of their dust data, BICEP2’s predictions were even more evidently premature.

Now, the Planck team has exhaustively gone over their data and BICEP2’s, and done a full analysis. The result is a pretty thorough statement: everything BICEP2 observed can be explained by interstellar dust.

A few news outlets have been describing this as “ruling out inflation” or “ruling out gravitational waves”, both of which are misunderstandings. What Planck has ruled out are inflation (and gravitational waves caused by inflation) powerful enough to have been observed by BICEP2.

To an extent, this was something Planck had already predicted before BICEP2 made their announcement. BICEP2 announced a value for a parameter r, called the tensor-scalar ratio, of 0.2. This parameter r is a way to measure the strength of the gravitational waves (if you want to know what gravitational waves have to do with tensors, this post might help), and thus indirectly the strength of inflation in the early universe.

Trouble is, Planck had already released results arguing that r had to be below 0.11! So a lot of people were already rather skeptical.

With the new evidence, Planck’s bound is relaxed slightly. They now argue that r should be below 0.13, so BICEP2’s evidence was enough to introduce some fuzziness into their measurements when everything was analyzed together.

I’ve complained before about the bad aspects of BICEP2’s announcement, how releasing their data prematurely hurt the public’s trust in science and revealed the nasty side of competition for funding on massive projects. In this post, I’d like to talk a little about the positive side of the publicity around BICEP2.

Lots of theorists care about physics at very very high energies. The scale of string theory, or the Planck mass (no direct connection to the experiment, just the energy where one expects quantum gravity to be relevant), or the energy at which the fundamental forces might unify, are all much higher than any energy we can explore with a particle collider like the LHC. If you had gone out before BICEP2’s announcement and asked physicists whether we would ever see direct evidence for physics at these kinds of scales, they would have given you a resounding no. Maybe we could see indirect evidence, but any direct consequences would be essentially invisible.

All that changed with BICEP2. Their announcement of an r of 0.2 corresponds to very strong inflation, inflation of higher energy than the Planck mass!

Suddenly, there was hope that, even if we could never see such high-energy physics in a collider, we could see it out in the cosmos. This falls into a wider trend. Physicists have increasingly begun to look to the stars as the LHC continues to show nothing new. But the possibility that the cosmos could give us data that not only meets LHC energies, but surpasses them so dramatically, is something that very few people had realized.

The thing is, that hope is still alive and kicking. The new bound, restricting r to less than 0.13, still allows enormously powerful inflation. (If you’d like to work out the math yourself, equation (14) here relates the scale of inflation $\Delta \phi$ to the Planck mass $M_{\textrm{Pl}}$ and the parameter r.)

This isn’t just a “it hasn’t been ruled out yet” claim either. Cosmologists tell me that new experiments coming online in the next decade will have much more precision, and much better ability to take account of dust. These experiments should be sensitive to an r as low as 0.001!

With that kind of sensitivity, and the new mindset that BICEP2 introduced, we have a real chance of seeing evidence of Planck-scale physics within the next ten or twenty years. We just have to wait and see if the stars are right…

# (Interstellar) Dust In The Wind…

The news has hit the blogosphere: the team behind the Planck satellite has released new dust measurements, and they seem to be a nail in the coffin of BICEP2’s observation of primordial gravitational waves.

Some background for those who haven’t been following the story:

BICEP2, a telescope in Antarctica, is set up to observe the Cosmic Microwave Background, light left over from the very early universe. Back in March, they announced that they had seen characteristic ripples in that light, ripples that they believed were caused by gravitational waves in the early universe. By comparing the size of these gravitational waves to their (quantum-small) size when they were created, they could make statements about the exponential expansion of the early universe (called inflation). This amounted to better (and more specific) evidence about inflation than anyone else had ever found, so naturally people were very excited about it.

However, doubt was rather quickly cast on these exciting results. Like all experimental science, BICEP2 needed to estimate the chance that their observations could be caused by something more mundane. In particular, interstellar dust can cause similar “ripples” to those they observed. They argued that dust would have contributed a much smaller effect, so their “ripples” must be the real deal…but to make this argument, they needed an estimate of how much dust they should have seen. They had several estimates, but one in particular was based on data “scraped” off of a slide from a talk by the Planck collaboration.

Unfortunately, it seems that the BICEP2 team misinterpreted this “scraped” data. Now, Planck have released the actual data, and it seems like dust could account for BICEP2’s entire signal.

I say “could” because more information is needed before we know for sure. The BICEP2 and Planck teams are working together now, trying to tease out whether BICEP2’s observations are entirely dust, or whether there might still be something left.

I know I’m not the only person who wishes that this sort of collaboration could have happened before BICEP2 announced their discovery to the world. If Planck had freely shared their early data with BICEP2, they would have had accurate dust estimates to begin with, and they wouldn’t have announced all of this prematurely.

Of course, expecting groups to freely share data when Nobel prizes and billion-dollar experiments are on the line is pretty absurdly naive. I just wish we lived in a world where none of this was at issue, where careers didn’t ride on “who got there first”.

I’ve got no idea how to bring about such a world, of course. Any suggestions?

# Insert Muscle Joke Here

I’m graduating this week, so I probably shouldn’t spend too much time writing this post. I ought to mention, though, that there has been some doubt about the recent discovery by the BICEP2 telescope of evidence for gravitational waves in the cosmic microwave background caused by the early inflation of the universe. Résonaances got to the story first and Of Particular Significance has some good coverage that should be understandable to a wide audience.

In brief, the worry is that the signal detected by BICEP2 might not be caused by inflation, but instead by interstellar dust. While the BICEP2 team used several models of dust to show that it should be negligible, the controversy centers around one of these models in particular, one taken from another, similar experiment called PLANCK.

The problem is, BICEP2 didn’t get PLANCK’s information on dust directly. Instead, it appears they took the data from a slide in a talk by the PLANCK team. This process, known as “data scraping”, involves taking published copies of the slides and reading information off of the charts presented. If BICEP2 misinterpreted the slide, they might have miscalculated the contribution by interstellar dust.

If you’re like me, the whole idea of data scraping seems completely ludicrous. The idea of professional scientists sneaking information off of a presentation, rather than simply asking the other team for data like reasonable human beings, feels almost cartoonishly wrong-headed.

It’s a bit more understandable, though, when you think about the culture behind these big experiments. The PLANCK and BICEP2 teams are colleagues, but they are also competitors. There is an enormous amount of glory in finding evidence for something like cosmic inflation first, and an equally enormous amount of shame in screwing up and announcing something that turns out to be wrong. As such, these experiments are quite protective of their data. Not only might someone with early access to the data preempt them on an important discovery, they might rush to publish a conclusion that is wrong. That’s why most of these big experiments spend a large amount of time checking and re-checking the data, communicating amongst themselves and settling on an interpretation before they feel comfortable releasing it to the wider community. It’s why BICEP2 couldn’t just ask PLANCK for their data.

From BICEP2’s perspective, they can expect that plots presented at a talk by PLANCK should be accurate, digital plots. Unlike Fox News, scientists have an obligation to present their data in a way that isn’t misleading. And while relying on such a dubious source seems like a bad idea, by all accounts that’s not what the BICEP2 team did. PLANCK’s data was just one dust model used by the team, kept in part because it agreed well with other, non-“data-scraped” models.

It’s a shame that these experiments are so large and prestigious that they need to guard their data in such a potentially destructive way. My sub-field is generally much nicer about this sort of thing: the stakes are lower, and the groups are smaller and have less media attention, so we’re able to share data when we need to. In fact, my most recent paper got a significant boost from some data shared by folks at the Perimeter Institute.

Only time will tell whether the BICEP2 result wins out, or whether it was a fluke caused by caustic data-sharing practices. A number of other experiments are coming online within the next year, and one of them may confirm or deny what BICEP2 has showed.

# Gravity is Yang-Mills Squared

There’s a concept that I’ve wanted to present for quite some time. It’s one of the coolest accomplishments in my subfield, but I thought that explaining it would involve too much technical detail. However, the recent BICEP2 results have brought one aspect of it to the public eye, so I’ve decided that people are ready.

If you’ve been following the recent announcements by the BICEP2 telescope of their indirect observation of primordial gravitational waves, you’ve probably seen the phrases “E-mode polarization” and “B-mode polarization” thrown around. You may even have seen pictures, showing that light in the cosmic microwave background is polarized differently by quantum fluctuations in the inflaton field and by quantum fluctuations in gravity.

But why is there a difference? What’s unique about gravitational waves that makes them different from the other waves in nature?

As it turns out, the difference all boils down to one statement:

Gravity is Yang-Mills squared.

This is both a very simple claim and a very subtle one, and it comes up in many many places in physics.

Yang-Mills, for those who haven’t read my older posts, is a general category that contains most of the fundamental forces. Electromagnetism, the strong nuclear force, and the weak nuclear force are all variants of Yang-Mills forces.

Yang-Mills forces have “spin 1”. Another way to say this is that Yang-Mills forces are vector forces. If you remember vectors from math class, you might remember that a vector has a direction and a strength. This hopefully makes sense: forces point in a direction, and have a strength. You may also remember that vectors can also be described in terms of components. A vector in four space-time dimensions has four components: x, y, z, and time, like so:

$\left( \begin{array}{c} x \\ y \\ z \\ t \end{array} \right)$

Gravity has “spin 2”.

As I’ve talked about before, gravity bends space and time, which means that it modifies the way you calculate distances. In practice, that means it needs to be something that can couple two vectors together: a matrix, or more precisely, a tensor, like so:

$\left( \begin{array}{cccc} xx & xy & xz & xt\\ yx & yy & yz & yt\\ zx & zy & zz & zt\\ tx & ty & tz & tt\end{array} \right)$

So while a Yang-Mills force has four components, gravity has sixteen. Gravity is Yang-Mills squared.

(Technical note: gravity actually doesn’t use all sixteen components, because it’s traceless and symmetric. However, often when studying gravity’s quantum properties theorists often add on extra fields to “complete the square” and fill in the remaining components.)

There’s much more to the connection than that, though. For one, it appears in the kinds of waves the two types of forces can create.

In order to create an electromagnetic wave you need a dipole, a negative charge and a positive charge at opposite ends of a line, and you need that dipole to change over time.

Change over time, of course, is a property of Gifs.

Gravity doesn’t have negative and positive charges, it just has one type of charge. Thus, to create gravitational waves you need not a dipole, but a quadrupole: instead of a line between two opposite charges, you have four gravitational charges (masses) arranged in a square. This creates a “breathing” sort of motion, instead of the back-and-forth motion of electromagnetic waves.

This is your brain on gravitational waves.

This is why gravitational waves have a different shape than electromagnetic waves, and why they have a unique effect on the cosmic microwave background, allowing them to be spotted by BICEP2. Gravity, once again, is Yang-Mills squared.

But wait there’s more!

So far, I’ve shown you that gravity is the square of Yang-Mills, but not in a very literal way. Yes, there are lots of similarities, but it’s not like you can just square a calculation in Yang-Mills and get a calculation in gravity, right?

Well actually…

In quantum field theory, calculations are traditionally done using tools called Feynman diagrams, organized by how many loops the diagram contains. The simplest diagrams have no loops, and are called tree diagrams.

Fascinatingly, for tree diagrams the message of this post is as literal as it can be. Using something called the Kawai-Lewellen-Tye relations, the result of a tree diagram calculation in gravity can be found just by taking a similar calculation in Yang-Mills and squaring it.

(Interestingly enough, these relations were originally discovered using string theory, but they don’t require string theory to work. It’s yet another example of how string theory functions as a laboratory to make discoveries about quantum field theory.)

Does this hold beyond tree diagrams? As it turns out, the answer is again yes!
The calculation involved is a little more complicated, but as discovered by Zvi Bern, John Joseph Carrasco, and Henrik Johansson, if you can get your calculation in Yang-Mills into the right format then all you need to do is square the right thing at the right step to get gravity, even for diagrams with loops!

This trick, called BCJ duality after its discoverers, has allowed calculations in quantum gravity that far outpace what would be possible without it. In N=8 supergravity, the gravity analogue of N=4 super Yang-Mills, calculations have progressed up to four loops, and have revealed tantalizing hints that the uncontrolled infinities that usually plague gravity theories are absent in N=8 supergravity, even without adding in string theory. Results like these are why BCJ duality is viewed as one of the “foundational miracles” of the field for those of us who study scattering amplitudes.

Gravity is Yang-Mills squared, in more ways than one. And because gravity is Yang-Mills squared, gravity may just be tame-able after all.

# Flexing the BICEP2 Results

There are lots of good sources on this, and it’s not really my field, so I’m just going to give a quick summary before talking about a few aspects I find interesting.

BICEP2 is a telescope in Antarctica that observes the Cosmic Microwave Background, light left over from the first time that the universe was clear enough for light to travel. (If you’re interested in a background on what we know about how the universe began, Of Particular Significance has an article here that should be fairly detailed, and I have a take on some more speculative aspects here.) Earlier experiments that observed the Cosmic Microwave Background discovered a surprising amount of uniformity. This led to the proposal of a concept called inflation: the idea that at some point the early universe expanded exponentially, smearing any non-uniformities across the sky and smoothing everything out. Since the rate the universe expands is a number, if that number is to vary it naturally should be a scalar field, which in this case is called the inflaton.

During inflation, distances themselves get stretched out. Think about inflation like enlarging an image. As you’ve probably noticed (maybe even in early posts on this blog), enlarging an image doesn’t always work out well. The resulting image is often pixelated or distorted. Some of the distortion comes from glitches in the program that enlarges the image, while some of it is just what happens when the pixels of the original image get enlarged to the point that you can see them.

Enlarging the Cosmic Microwave Background

Quantum fluctuations in the inflaton field itself are the glitches in the program, enlarging some areas more than others. The pattern they create in the Cosmic Microwave Background is called E-mode polarization, and several other experiments have been able to detect it.

Much weaker are the effect of the “pixels” of the original image. Since the original image is spacetime itself, the pixels are the quantum fluctuations of spacetime: quantum gravity waves. Inflation enlarged them to the point that they were visible on a large-distance scale, fundamental non-uniformity in the world blown up big enough to affect the distribution of light. The effect this had on light is detectably different: it’s called B-mode polarization, and this is the first experiment to detect it on the right scale for it to be caused by gravity waves.

Measuring this polarization, in particular how strong it is, tells us a lot about how inflation occurred. It’s enough to rule out several models, and lend support to several others. If the results are corroborated this will be real, useful evidence, the sort physicists love to get, and folks are happily crunching numbers on it all over the world.

All that said, this site is called four gravitons and a grad student, and I’m betting that some of you want to ask this grad student: is this evidence for gravitons, or for gravity waves?

Sort of.

We already had good indirect evidence for gravity waves: pairs of neutron stars release gravity waves as they orbit each other, which causes them to slow down. Since we’ve observed them slowing down at the right rates, we were already confident gravity waves exist. And if you’ve got gravity waves, gravitons follow as a natural consequence of quantum mechanics.

The data from BICEP2 is also indirect. The gravity waves “observed” by BICEP2 were present in the early universe. It is their effect on the light that would become the Cosmic Microwave Background that is being observed, not the gravity waves directly. We still have yet to directly detect gravity waves, with a gravity telescope like LIGO.

On the other hand, a “gravity telescope” isn’t exactly direct either. In order to detect gravity waves, LIGO and other gravity telescopes attempt to measure their effect on the distances between objects. How do they do that? By looking at interference patterns of light.

In both cases, we’re looking at light, present in the environment of a gravity wave, and examining its properties. Of course, in a gravity telescope the light is from a nearby environment under tight control, while the Cosmic Microwave Background is light from as far away and long ago as anything within the reach of science today. In both cases, though, it’s not nearly as simple as “observing” an effect. “Seeing” anything in high energy physics or astrophysics is always a matter of interpreting data based on science we already know.

Alright, that’s evidence for gravity waves. Does that mean evidence for gravitons?

I’ve seen a few people describe BICEP2’s results as evidence for quantum gravity/quantum gravity effects. I felt a little uncomfortable with that claim, so I asked Matt Strassler what he thought. I think his perspective on this is the right one. Quantum gravity is just what happens when gravity exists in a quantum world. As I’ve said on this site before, quantum gravity is easy. The hard part is making a theory of quantum gravity that has real predictive power, and that’s something these results don’t shed any light on at all.

That said, I’m a bit conflicted. They really are seeing a quantum effect in gravity, and as far as I’m aware this really is the first time such an effect has been observed. Gravity is so weak, and quantum gravity effects so small, that it takes inflation blowing them up across the sky for them to be visible. Now, I don’t think there was anyone out there who thought gravity didn’t have quantum fluctuations (or at least, anyone with a serious scientific case). But seeing into a new regime, even if it doesn’t tell us much…that’s important, isn’t it? (After writing this, I read Matt Strassler’s more recent post, where he has a paragraph professing similar sentiments).

On yet another hand, I’ve heard it asserted in another context that loop quantum gravity researchers don’t know how to get gravitons. I know nothing about the technical details of loop quantum gravity, so I don’t know if that actually has any relevance here…but it does amuse me.