Secrets of the Cosmic Microwave Background (Script) (Patreon)

Hook up an old antenna to your TV and scan between channels. The static buzz you hear is mostly due to the ambient radio produced by our noisy pre-galactic civilization. But around one percent of that buzz is something very different – it’s the cosmic microwave background radiation – the remnant of the heat-glow released when the hot, dense early universe became transparent for the first time. It sound likes random static, but that buzz contains an incredible wealth of hidden information. It holds the secrets of the universe’s fiery beginning, and of its final fate.

It’s not surprising that scientists have spent half a century and built multiple satellites to unlock the mysteries of the cosmic microwave background. We’ve delved into its nature before – from its formation 380,000 years after the Big Bang, to its 1964 discovery by Penzias and Wilson with the Holmdel Horn Antenna, to its increasingly accurate mapping across the sky with ever-better satellites. It all culminated in this – the Planck satellite’s map of the CMB.

Those blotches are tiny differences in temperature – deviations of one part in 10,000 from the average temperature of only 2.7 Kelvin. Those differences result from tiny variations in the density of matter right after the big bang, which evolved as colossal sound waves reverberated through the first few hundred thousand years of the universe’s life. We explored these baryon acoustic oscillations in last week’s episode, and that’s really worth watching first if you haven’t yet. 

That episode painted a simplistic picture. A quick review: in the very beginning, dark matter flowed towards tiny regions of increased density, drawn by gravity. Regular matter – what we call baryons - was in plasma form, with the simple atomic nuclei stripped of their electrons in the extreme heat. In this plasma state, light and matter were locked together. As the baryons compressed into over-dense regions, this led to a massive buildup of pressure. Collapsing baryons rebounded, producing a expanding sound wave.  That expanding shell was eventually frozen in place 380,000 later, when light decoupled from matter at the formation of the first atoms – the moment of recombination. As the universe evolved, those frozen shells collapsed into galaxies. We still see them today - interwoven pattern of rings, drawn in galaxies on the sky.

But those rings aren’t the whole story. Today we’re going to explore the intricate patterning, not of the galaxies, but of the CMB map: the image of the hot universe at the moment of recombination. We’ll see the complex dynamics of the early universe frozen into its spots. That patterning will tell us exactly what the universe is made of.

As I said, this picture of a single expanding shell of plasma is simplistic. In reality, these acoustic waves pulsed in and out of their local overdense region. They oscillated, and the number of oscillations depended on how large that overdensity was. In some places the overdensities were so large that matter only just had time to flow to the center before being frozen in place by recombination - no rebounding happened. And in other places the overdensities were smaller – the density wave had time to flow in, reverberate out, and then get captured by the gravitational field once more, falling back to the center. And that could happen multiple times.  Everywhere in the universe, the pull of gravity fought against the outward push of radiation pressure, causing density oscillations of all sizes. The state of those oscillations was frozen at the moment of recombination.

This messy, overlapping network of oscillations resulted in the spotty mess that is the map of the CMB. But crazily we can untangle that mess. We can do that by thinking of these complex oscillations as just a bunch of very simple oscillations of all different sizes stacked on top of each other. This only works because the differences between the highest and lowest density regions are so small. So in our calculations we model the early universe as many overlapping layers of simple density fluctuations. Each layer has .fluctuations of a certain size, defined by the mathematics of spherical harmonics – sort of like sine waves of different wavelengths but on the 2-D surface of sphere. The fluctuations in each of these layers oscillate independently, but by adding them together you can calculate the complex fluctuations of the early universe.

Thinking about the oscillations this way leads to a really powerful prediction. Over the 380,000 years between the big bang and recombination, each of our simple oscillators did its thing: sound waves moved inwards, outwards, inwards, outwards. When recombination hit, most oscillators were caught in the middle of an in- or outflow. Those aren’t the interesting ones. But some oscillators - those with just the right size - were caught either at maximum density – matter concentrated in the middle of the fluctuation, or at minimum density with matter at its most spread out. We call that second one maximum “rarefaction”. 

These particular oscillations define the most obvious spots on the CMB map because they were frozen in their extreme states. So the most prominent spots on the CMB will have exactly the right size to get a single collapse, or one collapse then one expansion, or two complete collapses, etc. The oscillations happened at the same speed: the speed of sound for our baryon-photon plasma, which was over half the speed of light. OK, so multiply the speed of sound by the age of the universe at recombination - that’s how far these density waves could travel. Divide that by the radius of a given density fluctuation to get how many half-oscillations it could execute. If the result is a whole number then that fluctuation size will be in an extreme state - either all in or all out - at the moment of recombination. So the sizes of these special spots should follow a harmonic series.

And that’s exactly what we see. The best way to show this is with what we call a power spectrum. It’s really just like a histogram that plots the number of spots of every possible size. And we definitely see that some sizes are more common than others. This peak here – those are spots in which the plasma only just had time to collapse once before recombination. The second peak corresponds to a full compression and then a full expansion. The third peak is for a compression then expansion then compression. And so on.

OK, nice, so we can explain the spot sizes. But what does this actually tell us about the universe? Kind of everything. In fact each of the peaks tells us something unique. Let’s go through them.

The main value of that first peak is as a measuring tape. Seriously. A standard ruler. Spots of this size represent fluctuations that had time to collapse exactly once, which means their size has to be equal to the speed of sound times the amount of time they had to collapse. Factoring in the expansion of the universe over that time, that size should be around half a million light years at recombination – theoretically. That gives us our ruler. Now, when we try to measure the size of those spots on the sky, we actually measure an angle. We need to convert to a distance using trigonometry. To do that we have to assume a flat universe. By flat I mean geometrically regular. Parallel lines stay parallel, and the angles of triangles add to 180 degrees. However the presence of matter and energy, as well as cosmic expansion, cause geometry to be curved, which would mess up our basic trig. So here we have a test: if we measure the angular size of these spots, use simple geometry, and that gives the exact physical size that we expect from our theory, that’s a good indication that the universe IS geometrically flat. And apparently it is. The spots are 1 degree on the sky, which corresponds to half-million-light year spots at recombination, just as predicted. To the limits of our ability to measure those sizes, the universe is flat.

That tells us something very important: it tells us the total amount of energy in the universe. Energy results in positive curvature due to its positive gravitational effect. On the other hand an expanding universe with no energy would have negative curvature. So a flat universe must have exactly the right amount of energy to flatten the geometry of the universe. So the first peak tells us the sum total of baryons, dark matter, and dark energy. We’ll see how useful that is when we look at the rest of the peaks.

OK, on to the second peak. That peak represents maximum rarefaction – fluctuations where matter had fully bounced out once after its initial collapse. To understand the use of the 2nd peak we need to use an analogy.  We can think of these oscillations as being like a heavy mass attached to a spring. Release the mass and it falls and then bounces up again, always back to its original position if it’s a perfect spring. But the heavier the mass, the further it’ll fall before bouncing up.

Think of the baryons as this mass – they’re heavy and want to fall towards our overdense spots. But the baryons are locked with light, which acts like our spring. The more baryons, the deeper matter will fall into that overdensity. Having more baryons should enhance the odd-numbered peaks, which represent the compressed state. On the other hand, the even-numbered peaks aren’t directly affected by the baryons – they represent the top of the spring’s rise, which is just determined by its starting position. What does that have to do with the 2nd peak? Well the more baryons, the higher the odd numbered peaks are compared to the even numbered peaks. In practice, we can just use the height of the second peak relative to the first peak to measure the baryon content of the universe. And those measurements tell us that baryons constitute only about 5% of the total energy in the universe.

And finally we get to the other peaks, representing smaller fluctuations. These tell us about the dark matter.  More accurately they tell us about the relative amount of dark matter compared to radiation. This is a bit too much of a rabbit hole for right now – but in short: in the first few tens of thousands of years, the universe was in the radiation-dominated epoch. Basically, photons produced more gravity than matter. Fluctuations that were small enough  to oscillate at least once during that brief time should be enhanced – their peaks on the power spectrum should be raised compared to larger fluctuations. So by looking at the height of those peaks you can actually figure out when the radiation epoch gave way to the dark matter-dominated epoch. That in turn tells you how much dark matter there is. Spoiler: there’s a lot.

OK, let’s bring this together: size of the spots in the first peak tells you the total amount of dark energy, dark matter, and baryons. The second peak gives you just the amount of baryons, and the higher peaks give you the amount of dark matter. Combining we can separate the relative content of all three components. Extrapolate that to the modern universe, and we get that baryons constitute only 5% of all mass and energy. That’s all the atoms in all the stars in all the galaxies, basically everything you can see. The remaining 95% is the so-called dark sector. Dark matter is 26.5%, and dark energy is a whopping 68.5%. This is a super important verification, because we get approximately the same numbers when we look at the dark matter content in modern galaxies and clusters, and the dark energy based on measuring the accelerating expansion rate of the universe.

So that’s how you lay bare the secrets of the cosmic microwave background. It’s an insane wealth of information from what look like random, miniscule fluctuations in this faint, noisy buzz. So next time you hear the static whisper of an untuned TV or radio, remember that in that noise can be found the secrets to the earliest epoch of space time.