What Can The CMB Tell Us? – Part I

So it turns out that last week’s choice of the CMB as a topic was a particularly presient one, as this week’s science news is dominated with a story that has a lot to do with these all-important photons. If it proves to hold up to scrutiny, BICEPs detection of B-Mode gravitational waves may be the biggest physics story of the year. It has implications for theories of inflation, the big bang and even quantum gravity. It even may be the first sign on our roadmap to a “grand unified theory”, and it all comes from the Cosmic Microwave Background!
As promised, this week I will be explaining how and what we measure when we look at the CMB, and what that can tell us about the history of our universe and what we can discover about the universe we live in today. However, the idea behind this blog is to cover The Interesting Part of the science stories making the headlines, and the fact is that The Interesting Part of BICEPs potential discovery is… well… all of it! So in the next couple of days I’m also going to try and write some bonus posts on topics such as Gravitational Waves, Inflation and Energy Scales, to try and get to the heart of why BICEPs results have the potential to be so important.

For more information of BICEPs results see here and here, and for analysis of what it means and why we shouldn’t get TOO excited about it yet, see here and here. Now, on with the CMB!

If you recall, last week we left our photons suddenly unencumbered by charged matter, free to stream across the universe at will. Eventually they reach us, we can detect them and measure some of their properties. Photons are pretty basic objects, and they really only have two useful properties: Their energy or temperature (which is tied to their wavelength) and their polarization. It is the latter that turns out to be important for BICEP’s results, but it the former is simpler so we’ll look at that first.

If we point our telescopes at the sky, we mainly see stars and planets and gas clouds and dust. We can use a variety of techniques to remove these things, and what we’re left with is…surprisingly boring, at least at first glance. What we see is a whole load of photons across the whole sky, all at the same temperature, 2.7 Kelvin. This is the cosmic microwave background, as we measure it today.

While at first glance this seems kind of anticlimactic, it actually tells us quite a bit about the universe we live in. Firstly, 2.7 Kelvin is a remarkably cold temperature. It is only a few degrees above absolute zero. How could the chaotic boiling soup of particles that I described last week lead to such cold, un-energetic photons? How did they lose all that energy? To answer this question, we have to recall that the energy of a photon is tied to its wavelength. A higher wavelength means a lower energy, and vice-versa. We also have to recall a measurement made by Edwin Hubble in 1929. He showed that distant galaxies were receeding from us, providing the first evidence that the universe was expanding.

This means that as the photons of the CMB move through the universe as the universe itself expands. This is a bit of a weird concept, so I will take a few moments to try to clarify. You may have heard that the universe is expanding and imagined all the objects (stars, galaxies, planets, chocolate bars, socks, etc.) simply getting further apart, moving from one part of space to another, more distant part of space. This is almost correct, but not quite. Instead space ITSELF is expanding. The classic analogy for this is two dots drawn with marker on a balloon. As the balloon is inflated, the two dots move further apart. They haven’t moved their positions on the balloon, there is simply MORE space between them now.

Now imagine drawing a wavy pattern, like this

on the balloon. As you inflate the balloon, the peaks of the wave move further apart. Its “wave-length” has increased This is exactly what happens to our poor old photons as they travel across the universe: they get stretched out, and lose energy.

So now we know why our photons are so cold! Because space is expanding! A pretty exciting conclusion that we can draw from what seems like a mundane measurement. In fact, this measurement yields another incredible conclusion about our universe. Lets look at it a little bit more closely.

The photons cover the whole sky, every single one of them at a temperature of 2.7 Kelvin. The difference in temperature between the hottest photon in the CMB and this average is less than 0.000001 Kelvin. This is a fascinating fact: all these photons are so close to one another in temperature, no matter where we measure. This tells us something very profound about our universe. It forces us to ask the question, what possible conditions could there be which would cause the universe to be full of photons all with exactly the same temperature?

In order to make two things the same temperature in daily life, they have to be put in contact. You have to put your pot of pasta on the hotplate for it to cook. It won’t do it from the other side of the room. Similarly, the photons need to be in thermal contact for them to reach the same temperature. In this case, the contact isn’t physical, as with the hotplate and the pot, but simply a way of saying that the photons must be close enough to influence one another. What determines how close they need to be? Well, a combination of two simple things: The amount of time they have, and the speed they can travel. The speed that a photon can travel is, unsurprisingly, light speed. The amount of time the photons have is a little over 300,000 years (the age of the universe at the time that the CMB was formed, as discussed last week). This seems kind of reasonable. Over such a long time period, things may be able to settle down to be the same temperature.

However, things are complicated by the fact that the universe is expanding. If we take the current size of the universe and the current age of the universe, we can work out how fast it would have to expand from the big bang to be its current size. It turns out that at around the time the CMB was being made, the universe would have been expanding at faster than the speed of light! The universe is just so large, and not THAT old! This is perfectly possible within general relativity, but it does mean that two areas of the universe separated in space would have no way of communicating! For every meter a photon from one side travels, the other side will have moved two meters away due to the expansion of the universe! There’s no way, in this case, for the photons to be in thermal contact, and hence no way for them to reach the same temperature.

The solution to the problem is a concept known as “inflation” by cosmologists. What this means is that shortly after the Big Bang, the universe underwent a very rapid period of expansion, expanding much MUCH faster than the speed of light. After this period, the universe settled down, expanding at a rate much slower than the speed of light. This allows for both the current large size of the universe compared to its age by having it be already quite large very soon after the big bang. Then the photons can move into thermal equilibrium (aka being the same temperature) without having to worry about the universe expanding too fast.

So the low temperature of the CMB tells us the universe is expanding, and the uniformity of that temperature gives us evidence for how that expansion occurred. Not bad for a seemingly boring result. And it turns out there’s even more we can learn from the CMB if we look a little closer.

Recall that the photons of the CMB are all the same temperature up to about 1 part in 100000. But there are variations. Tiny variations, but they exist. If we can get an understanding of where these variations might come from, can learn even more about our universe.

One of the tenets of quantum mechanics is that no field is free from variations. Even in its ground (or lowest energy) state, a quantum field’s energy will vary at random. These variations are often small, but there is no way of removing them. In the early universe the two dominant fields were gravity (more on this later!) and the field which powered inflation: the so-called “inflaton”. When the inflationary epoch was over, the inflaton field broke apart (or decayed) into the particles that make up all the matter in the universe. In a non-quantum universe, these particles would be evenly distributed. The same amount of particles in each part of space. But due to these unavoidable quantum fluctuations, some parts of the inflaton field will be at a slightly higher energy than other parts. This means that when it decays, the high energy parts will produce a few more particles than the low energy parts. So some regions of space will have a couple more particles, while other areas will have a few less. These variations are what eventually give us the temperature variations in the CMB.

So now we have a sea of particles which is nearly, but not quite uniformly distributed. Those places which have slightly more particles have a slightly stronger gravitational pull, because they’re simply a little bit heavier. These particles start to attract one another, moving closer together. However, has they get closer the electromagnetic force between them gets stronger. Recall, these particles are mainly protons and electrons, which have opposite charges, so they repel. The electromagnetic force slows down their approach until they start to push apart again. They move apart until gravity once more overcomes electromagnetism and the particles start to move closer once more. Its like bouncing a ball, it goes until the floor (in this case electromagnetism, or “photon pressure”) stops it, then starts to go back up until gravity turns it around again. And, much like a bouncing ball, the energy the particles have depends on where in the cycle they are. A bouncing ball is at its slowest at the top of its path, right before it starts to drop. It’s at its fastest as it nears the floor. In exactly the same way, the particles are at their most energetic, their hottest, as they get closer together, and at their coldest as they get further away. Their temperature is determined by the part of the cycle they’re in They keep repeating this cycle, over and over, until..…POP! The particles form into neutral atoms (“recombination”), and the electromagnetic forces are nullified, stopping the cycle in its tracks.

What does this mean for the photons? Well, remember that the electrons & protons are in thermal equilibrium with the photons. As the particles get hotter, the photons do too. And when the particles suddenly snap into neutral atoms, the newly freed photons have the same temperature as the particles that were surrounding them at that moment. This means that when we measure them, we can tell exactly what part of the hot-cold cycle the particles in that region were in when “recombination” occurred.

This allows us to determine some very important things about the universe. You see, the speed at which the particles go through this bouncing cycle of hot-to-cold is dependent on their density: how many of them there are in a particular space, and also on their composition: how many protons vs electrons vs dark matter particles etc., etc. there are. While the whole universe will be made up of roughly the same composition of particles, the density varies, as discussed above. There will be some parts of the universe where the particles are just dense enough to go from cold to hot before recombination, and some areas where they have time to go from cold to hot and back to cold, or cold-hot-cold-hot. If we look for at areas of the CMB where the hottest photons are, we can determine that those areas are the ones that only went once through the cycle. If we look at where it is coldest, we see the parts which went through the cycle cold-hot-cold. If we then measure how much space these areas take up, we can determine the density required to make one of these cycles would be. If we know the density of all the regions of space, and we know how big the universe was at the time, we can calculate the composition of matter in the universe. Although the density has changed as stars and planets and socks and cars are formed, the composition must stay the same.

Just from looking at these tiny variations in temperature, we can tell how much matter is in the universe, how much of it is dark matter, how much of it is regular matter, how much dark energy there is. From looking at a boring field of nearly identical photons, we can tell how our whole universe started, where its going, and what its made up of.

If we look at how those photons are polarized, we can tell even more.. more on that later!

Thanks for reading,

McC

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