So in my mind the axis is caused both by imperfect experiments and analysis and by the human need to find patterns…

So in my mind the axis is caused both by imperfect experiments and analysis and by the human need to find patterns in everything.

Originally shared by Jonah Miller

The CMB Axis of Evil and the Nature of Randomness

This Halloween, Nature News & Comment  released an article titled Zombie Physics: 6 Baffling Results that Just Won’t Die. It’s a fun article describing several mysteries in physics whose solution sits in a sort of limbo.

For fun, I figured, I’d explain some of these mysteries, and give my opinion about possible solutions. I’ll tag them under #ZombiePhysics .  First, I’m going to discuss the CMB Axis of Evil, a strange pattern in the leftover radiation from the Big Bang.

(Those of you who wish to read my post in blog form can do so here: http://www.thephysicsmill.com/2015/10/31/the-cmb-axis-of-evil-and-the-nature-of-randomness/)

A Much-Too-Short Summary of Cosmic Inflation and the CMB

About 13.8 billion years ago, the universe was extremely hot, so hot that matter couldn’t form at all… it was just a chaotic soup of charged particles. Hot things (and accelerating charges) glow. And this hot soup was glowing incredibly brightly. As time passed, the universe expanded and cooled, but this glow remained, bathing all of time and space in light.

(The reason for why the universe was so hot in the first place depends on whether cosmic inflation is true. Either it’s because the Big Bang just happened or it’s because, after cosmic inflation, a particle called the inflaton dumped all of its energy into creating hot matter.)

Even today, the glow remains, filling the universe. As the universe expanded, the glow dimmed and its light changed colors (due to gravitational redshift, see: http://www.thephysicsmill.com/2013/03/24/receding-horizons-dark-energy-and-the-expanding-universe/), until it became microwaves instead of visible or ultraviolet light. This ubiquitous glow is called the Cosmic Microwave Background, or CMB [1] for short, and if you turn an old analogue TV to an unused channel, some of the static you hear is CMB radiation picked up by your TV antenna [2].

Since its discovery, the CMB has been one of our most powerful probes of cosmology. It lets us accurately measure how fast the universe is expanding [3], the relative amounts of normal stuff vs dark energy and dark matter [4], how the density of matter fluctuated in the early universe [5], how the Earth is moving relative to the expansion of the universe [6], and much more.

Some parts of the early universe were more dense and some were less, and this translates to slight, random variation in the color of light in the CMB. And in turn, we can translate this into a temperature. The temperature of the CMB is incredibly consistent across the sky. It’s an almost perfect 2.725 Kelvin. However, there are tiny fluctuations relative to this mean, and these reflect the dynamics of the early universe. Figure 2 shows a map of these fluctuations and I describe how this map is attained in my post on BICEP2: http://www.thephysicsmill.com/2015/02/01/bicep2-result-just-dust-thats-okay/

The CMB Axis of Evil

It’s very hard to see in figure 2, but with a little massaging, we can see that many of the fluctuations in the CMB align along a single axis, called the axis of evil, as shown in figure 1. (Formally, the quadrupole and octopole moments of the fluctuations align.) At first glance, is quite strange, because we believe that the fluctuations in the density of the early universe should be randomly distributed in a particular way… and this is exactly the way they are distributed on smaller scales. The mottled look of figure 2 is exactly due to this particular random behaviour of the fluctuations in the CMB.

So what’s going on? There are a couple of possibilities. I’ll go over them and add my opinion (and the scientific consensus or lack thereof).

Errors in Foreground and Modelling

Perhaps the most boring explanation is that we made a mistake when creating the CMB maps like figure 1 and figure 2. As the story of BICEP2 [7] shows, making those maps is very hard. To create them, we have to account for all the other sources of microwave radiation in the universe and carefully remove them from our measurements.

Over time, we’ve gotten incredibly good at this…so good that we can extract all sorts of information about the early universe from the CMB. But that doesn’t mean we’re always right. There could be extra dust in the solar system [8]. Or a confluence of the gravitational pull of distant galaxies on the light of the CMB (called the integrated Sachs-Wolfe effect) could magnify a normal random fluctuation so that it appears significant [9].

(I am really oversimplifying the integrated Sachs-Wolfe effect here. But that’s a story for another time.)

I think errors in foreground modelling could easily account for the axis of evil.

The Universe is a Doughnut or a Sphere

Imagine an ant living on the surface of a doughnut. The ant is so small that the doughnut appears flat to it. As the ant travels forward, it will eventually return to where it started, no matter what direction it travelled. From our perspective, of course, this is because a doughnut wraps around. But to the ant, this would be quite mysterious! Figure 3 shows the doughnut from both our perspective and the ant’s perspective. This is very similar to how if you travel East on the Earth, you eventually return to your starting place.

What if our universe was like the doughnut, but in three dimensions? So if you start going in a direction, say towards Andromeda, and keep going for as long as possible, billions of light years, you would eventually get back to where you started (ignoring of course that the universe is expanding and thus the distance you would have to travel would increase faster than you could travel it).

What if, perhaps we see the same things on both sides of the axis of evil because they are literally the same things and the universe has wrapped around on itself? In the original paper discussing the axis of evil [10], the authors discuss this very possibility. It’s a nice idea, but it can actually be tested by trying to match images of stars and galaxies (and fluctuations in the cosmic microwave background) on opposite sides of the sky to see if they look the same. The results, however, are not favourable. So no one takes this idea very seriously… even though it’s very clever.

Cosmic Variance

This one takes a bit of explanation. So bear with me. First, let’s talk about something called a posteriori statistics.

A Posterioiri Statistics

Imagine a teacher breaks her students into two groups. She tells one group to flip a coin ten times and record the result as a sequence of heads or tails. The group might record, for example,

HHHHTTTTHT

which would correspond to a string of four tails, then a string of four heads, then one head, and one tail. She tells the other group of students to make up ten coin flips, but try to do so in a way that looks random. The two collections the students return are:

THTTHTHHTT

and

TTHHHHTHTH

And, masterfully, the teacher immediately picks out the truly random sequence.  Which one is it? How does she do it? The second sequence, TTHHHHTHTH, which looks very structured, is the random one.

The human mind is very good at picking out patterns, and attributes a cause to every pattern it sees. But random numbers, very naturally, randomly in fact, appear to make patterns, even though the pattern doesn’t mean anything. It’s just random noise. The teacher takes advantage of this. She knows her students will avoid creating a sequence that looks too structured, because they don’t think random numbers look like that. But random numbers can easily look like that.

Of course, the probability that precisely the second sequence would emerge is less than one percent. But the emergence of some sequence that looks vaguely like the second sequence is vastly more likely.  You can think of this like finding a cool looking cloud, or Jesus in your morning toast. You see the cool looking cloud and you think “Wow! A cloud that looks like an airplane! What are the odds?” But you should be thinking “Wow! A cloud that looks like an airplane! The odds of me finding a cloud that looks like something interesting are quite high because there are a lot of clouds and a lot of things I think are interesting.”

This sort of thinking is called a posteriori statistics. And in general, it causes mistaken analysis.

The CMB Axis of Evil

So what does this have to do with the CMB? Well, people who study the CMB are well aware of the danger of a posteriori statistics, so they try to avoid thinking in this way. One way to avoid this sort of thinking is to make many many measurements. If you have a huge number of sequences of coin flips, on average, the randomness (or lack thereof) will become manifest.

And this is indeed what we do for most of the cosmic microwave background. The fluctuations on small scales, which give figures 1 and 2 their mottled texture, are numerous and we can do many statistics on them by looking at different areas of the sky.

But the axis of evil is different. It covers almost the whole sky. And we only have one sky to make measurements of! So it’s not possible to do good statistics. The fact that we have only one universe to measure, which we believe emerged from random processes, and that we can’t do statistics on a whole ensemble of universes is called cosmic variance.

And cosmic variance interferes with our ability to avoid a posteriori statistics. It lets us fool ourselves into believing that the way our universe turned out is special, when there may in fact be a multitude of equally probable ways our universe could have been. And it is entirely possible that the axis of evil is one such “fluke.”

It is possible, in principle, to reduce the effects of cosmic variance. If we could move to another position in the universe, we would be able to see a different portion of the CMB (because the light that could have reached us since the CMB was created would come from a different place in the universe). In 1997, Kamionkowski and Loeb [11] suggested using the emissions of distant dust to extrapolate what the CMB looks like to that dust. In principle, it would be possible, but very very hard, to use this trick to test whether or not the axis of evil comes from cosmic variance.

As you may have guessed from the amount of time I devoted to the explanation, I find cosmic variance to be a very compelling cause of the axis of evil.

The Most Likely Story, In My Opinion

So… what do I think is the cause of the axis of evil? The following is my opinion and not rigorous science. But it went something like this. Due to random fluctuations in the way the universe could have been, something that looks like the axis of evil formed in the CMB, but much less significant. This would be the cosmic variance explanation. To this day, the “axis of evil” remains statistically insignificant. But, because our models of cosmic microwave sources and filters look like in the universe and in our solar system are flawed, and because we don’t take the integrated Sachs-Wolfe effect into account, the axis of evil appears much bigger to us than it actually is.

So in my mind the axis is caused both by imperfect experiments and analysis and by the human need to find patterns in everything.

Acknowledgements

I owe a huge thanks to my friend and colleague, Ryan Westernacher-Schneider, who told me this story last spring and compiled a summary and list of references. Ryan basically wrote this blog post. I just paraphrased and summarized his words.

Further Reading

I’m not the first science writer to cover this material. Both Ethan Siegel  and Brian Koberlein  have great articles on it. Check them out:

1. This is Brian Koberlein’s article:

https://briankoberlein.com/2014/08/25/anomalous-anomalies/

2. This is Ethan Siegal’s:

https://medium.com/starts-with-a-bang/ask-ethan-85-hubble-vs-the-big-bang-8b26ef0fdfb6#.lhqhcz4ip

For those of you interested in reading about the axis of evil in more depth. Here are a few resources.

1. This is the first paper to discuss the axis of evil. It also discusses the possibility that the universe is a doughnut:

http://arxiv.org/abs/astro-ph/0307282

2. This paper coined the term “axis of evil.”

http://arxiv.org/abs/astro-ph/0502237

3. This paper discusses the possibility of solar-system dust producing the axis of evil:

http://arxiv.org/abs/0910.1317

4. This paper discusses the integrated Sachs-Wolfe effect and how it enhances the axis of evil:

http://arxiv.org/abs/0909.2495

5. This paper proposes a way of reducing cosmic variance:

http://dx.doi.org/10.1103/PhysRevD.56.4511

6. This is the collected published results by the Planck collaboration, which analyses all aspects of the CMB in great depth:

http://www.cosmos.esa.int/web/planck/publications

Inspiration

1. You can read the nature article on zombie physics here:

http://dx.doi.org/10.1038/nature.2015.18685

2. I also wrote a post about the Nature article here:

https://plus.google.com/+JonahMiller/posts/fACHMX3gXZ7

Related Reading

If you enjoyed this post, you might enjoy my other posts on cosmology. I wrote a two-part series on the BICEP2 experiment:

1. In the first article, I describe what BICEP2 was claiming to observe:

http://www.thephysicsmill.com/2014/03/18/bicep2-primordial-gravity-waves-cosmic-inflation/

2. In the second article, I describe how measurements of the CMB are made and what went wrong with BICEP2:

http://www.thephysicsmill.com/2015/02/01/bicep2-result-just-dust-thats-okay/

I have three-part series on the early universe:

1. In the first article, I describe the evidence for the Big Bang:

http://www.thephysicsmill.com/2013/05/12/always-walk-away-from-an-explosion-the-story-of-the-big-bang/

2. In the second article, I describe problems with the Big Bang theory:

http://www.thephysicsmill.com/2013/06/09/a-mess-of-cosmic-coincidences-problems-with-big-bang/

3. And in the third article, I describe cosmic inflation and how it fixes the problems we had with the Big Bang:

http://www.thephysicsmill.com/2013/06/26/fixing-the-early-universe-cosmic-inflation/

I have a fun article that describes the cosmic microwave background as the surface of an inside-out star:

http://www.thephysicsmill.com/2015/02/14/universe-inside-star/

References

[1] https://en.wikipedia.org/wiki/Cosmic_microwave_background

[2] http://www.universetoday.com/25560/the-switch-to-digital-switches-off-big-bang-tv-signal/

[3] https://en.wikipedia.org/wiki/Hubble%27s_law

[4] http://en.wikipedia.org/wiki/Dark_matter#mediaviewer/File:080998_Universe_Content_240_after_Planck.jpg

[5] https://en.wikipedia.org/wiki/Baryon_acoustic_oscillations

[6] http://en.wikipedia.org/wiki/Cosmic_microwave_background#CMBR_dipole_anisotropy

[7] http://www.thephysicsmill.com/2014/03/18/bicep2-primordial-gravity-waves-cosmic-inflation/

[8] http://arxiv.org/abs/0910.1317

[9] http://arxiv.org/abs/0909.2495

[10] http://arxiv.org/abs/astro-ph/0307282

[11] http://dx.doi.org/10.1103/PhysRevD.56.4511

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