What does the sound of the Big Bang look like?

Six weeks ago I wrote a post where I tried to explain how we know that the Big Bang definitely happened. There are of course other reasons why we know the Big Bang happened, but I decided to focus on one, relatively easily explained piece of evidence, which is the existence and frequency spectrum of the Cosmic Microwave Background (CMB).

Quickly summarising: The CMB is very cold radiation that permeates the entire universe. It was created when the expanding and cooling universe cooled to a point where it was cold enough for hydrogen atoms to form. Before this point, the electrons and protons in hydrogen had enough energy to be free from each other to form an opaque plasma. Once neutral hydrogen formed the universe became transparent and the CMB was formed and travelled (almost) freely forever after. We have detected and measured this CMB and its intensity as a function of its frequency (effectively, the brightness of each colour) is exactly what the Big Bang predicted. If there was no Big Bang there would be no reason to expect a CMB to exist, let alone for it to have this particular property. For more details please read my previous post and the links within.

When writing that post I had intended to say quite a bit more about the CMB and the Big Bang than I ended up having space for. It is not quite true that the mere existence (and spectrum) of the CMB is enough to conclusively determine that the Big Bang must have happened. However the existence of the CMB did build the metaphorical equivalent of a thousand big, bold and bright neon signs that all pointed aggressively towards the Big Bang being true.

When I began writing that earlier post and claimed that the CMB does conclusively prove that the Big Bang happened I had in my mind what I actually discuss in this post. This is the fact that we can see in the CMB the effects of sound waves that existed in the primordial hydrogen plasma. It is these sound waves and our measurements of them that puts the final nail in the coffin of all things not the Big Bang. They also represent what I claimed in that earlier post to be “jaw-droppingly stunning pieces of detective work”.

The glorious Planck satellite, measurer of all things CMB

Sound waves in the primordial hydrogen plasma

At the time that the CMB formed the ever-interesting hydrogen plasma had been minding its business for around 400,000 years. As I stressed in the previous post, the temperature in this plasma was constant everywhere. However, the density of the plasma wasn't quite. There were tiny, tiny imperfections (around one part in 10^{-5}). We know that these density fluctuations must have existed simply because we exist. That is, because stars exist, galaxies exist and clusters of galaxies exist. None of these things could have existed if the primordial hydrogen was completely uniform because they came from that hydrogen. However these structures took billions of years to form, so the fluctuations must have been very small.

Let's try and get some perspective as to just how smooth the density was in this primordial hydrogen plasma. Suppose you took two buildings, each 100 metres tall, and made one of them just one millimetre taller. Then comparing the density of the hydrogen plasma from one point to another is equivalent to comparing the heights of these two buildings.

These tiny density fluctuations in the hydrogen didn't remain stationary for all 400,000 years. Firstly, the universe was expanding. Therefore, the overall density of every region in the plasma was dropping. Moreover, the slightly over-dense regions had a slightly greater gravitational attraction than the under-dense regions. Therefore, just as I explained here, when discussing the formation of galaxy clusters, the density fluctuations at these points initially grew. However, unlike the example with the galaxy clusters where there is nothing except gravity, the hydrogen plasma is full of radiation. As the density fluctuation in a region grew so did the pressure in this radiation and this pressure acted to push the region apart. Eventually, the density fluctuation stopped growing under gravity and started falling because of this pressure. However, as soon as this happened, the pressure started to drop. Eventually, the pressure dropped enough that gravity was again the stronger force. Then, the density started to increase again and the process was repeated. And so on, and so on...(An exactly analogous effect was occurring in the initially under-dense regions.)

This was what happened in the hydrogen plasma for those 400,000 years. The density fluctuation in any region rose and fell, rose and fell as first gravity and then pressure took their turn in pulling and pushing matter towards and away from this region of the plasma. This pulsation in the hydrogen plasma created tiny ripples that propagated through the plasma. These ripples were sound waves and were just like the sound waves that propagate through air. 

You might be tempted to ask “what would these sounds waves have actually sounded like?” Unfortunately, the answer to this question is not particularly interesting. Firstly, they were far too quiet for the human ear to hear. Secondly, their frequency was far too low to be audible by the human ear. And finally, they didn't have a clear tone (they were made up of many different frequencies). So, even if they were made louder and brought into an audible frequency range, they would not have sounded much different to noise. Nevertheless, this guy claims to have made them louder and audible – so have a listen – but be prepared to be underwhelmed.

The Acoustic Peaks

I mentioned above that the pulsation of over-density to under-density to over-density to under-density occurred in any given “region” of the plasma. Well, how big were these “regions” that I'm talking about? The answer is, in fact, “all sizes”.

OK that's a bit confusing, so let me try to explain. If I choose to look at any region in the hydrogen plasma with any arbitrary size then it will either be slightly more dense or slightly less dense than the average density of the entire plasma. In which case, everything I wrote above about the pulsation of this density fluctuation holds. Of course, if you were to look at this region more closely, you would see that smaller regions inside it were also pulsating. That's fine, so long as the average density fluctuation over all of these smaller regions corresponds to the density fluctuation of the larger region encompassing them.

Now come the most important two paragraphs of this entire post, so concentrate hard.

Smaller regions will pulsate from over-dense to under-dense more rapidly than bigger regions. Why? Well, because any physical effect in the plasma takes time to propagate through it (the speed at which these physical effects propagate is the speed of sound in the plasma). This means that if a region is smaller it will take less time for any physical effects occurring in it to propagate from one side to the other. Therefore, the interchange between gravity and pressure in a small region can occur more rapidly. OK?

Now, remember that the hydrogen plasma only existed for a finite length of time (approximately 400,000 years). Therefore, when the CMB formed, there was some particular size in the universe, such that all regions of that size would have had just enough time to reach the maximum over-density possible. That is,  the CMB formed just before radiation pressure began to push these regions apart again.

I said those paragraphs were crucial. Here is why. If at precisely the moment that the CMB was formed we were somehow able to measure the density fluctuation in regions with that particular size then we would expect it to be characteristically larger than the density fluctuation in regions of any other size. This is a highly non-trivial thing to be able to expect.

The characteristic length just described is called the sound horizon. It takes this name because it is precisely the distance sound could have travelled since the Big Bang began. The peak in the density fluctuations at this characteristic length is suitably called an “acoustic peak”.

How does all of this affect the CMB?

Let's go back to every cosmologist's best friend, the CMB. As you now know, The CMB forms when the hydrogen in the universe becomes neutral and the light in the universe stops interacting with the hydrogen through electric forces. However everything in the universe continues interacting gravitationally. The density fluctuations discussed above were tiny (remember the analogy to the buildings), but they were definitely there. Due to gravity, the slightly over-dense regions are slightly more attractive than the slightly under-dense regions. Therefore, any of the light in the CMB that happened to form in a slightly over-dense region will lose a tiny bit of its energy as it escapes that ever so slightly greater gravitational pull. Equivalently, the light in the CMB that came from under-dense regions will actually gain a little bit of energy as it is pulled out of the under-dense region. These tiny gains and losses of energy in the CMB turn into tiny increases and decreases in the temperature of the CMB. Tiny increases and decreases in the temperature of light basically correspond to tiny changes in its colour (very loosely speaking - hotter light is bluer and colder light is redder).

This is remarkable and extremely fortuitous for those of us wanting to study the early universe. If we can measure the temperature of the CMB today accurately enough to detect these tiny fluctuations in temperature then we are directly measuring those tiny density fluctuations in the primordial universe. Astonishing. This means that everything I just wrote about those density fluctuations is directly measurable in the CMB. In particular, if we look carefully enough at the CMB, we can actually see the primordial sound waves of the universe. Read again what I just wrote. It wasn't a metaphor. The CMB is light. When we record the CMB today we are basically taking a photograph of what the early universe looked like. It just took 13.7 billion years for the light to reach the camera! (I'm not quite sure what “impossible images” are but the sound of the Big Bang surely must make the short-list of the most remarkable images ever recorded by humanity.)

The best image we have of the temperature fluctuations in the Cosmic Microwave Background (WMAP).

Making this measurement, that is, taking this photograph accurately enough that these fluctuations in the temperature of the CMB are actually visible (remember the analogy of the buildings) has taken humanity some time. The CMB itself is very cold (2.7 Kelvin), therefore tiny fluctuations in this temperature are exceedingly small. To measure these fluctuation we need to measure the temperature of the CMB to an accuracy better than 20 micro Kelvin. That is very cold. For context, absolutely nowhere in space is that cold. In fact, quite possibly the only places in the entire universe that are that cold are in physics laboratories on planet Earth (but I guess that is a story for another post).

COBE, the satellite experiment I mentioned in my previous post, was the first experiment ever to be able to measure the temperature accurately enough to see these fluctuations. It took what is now a relatively low resolution version of this photograph (but enough for a Nobel prize at the time!). Later experiments, that were based out of hot-air balloons then took higher resolution versions of this photograph, but could only see small fractions of the sky. Today's most significant version of this photograph comes from the WMAP satellite which made its measurements in the first decade of this century. Now, the entire cosmological community awaits the results from the Planck satellite, which is up in space measuring the CMB right now and will improve the resolution of this photograph even further.

The image above is the WMAP version of the photograph, covering the entire sky. The fluctuations have been scaled up in amplitude considerably in order to make them visible. The true version of this photograph without rescaling looks like this (remember the analogy of the buildings – could you see the difference in those buildings just by looking at them?). Also, keep in mind that the CMB is not visible to the human eye, even if it is visible to the “camera” taking the photograph. The colours in this image are chosen to represent what the CMB would look like if its colours were in the visible part of the colour spectrum. Confusingly, the redder the image is, the hotter that part of the sky is and the bluer it is, the colder. I know, I know I sad earlier that the reality is the opposite – don't blame me, blame the people at WMAP! (or more accurately, the people in history who made the arbitrary decision that red=hot and blue=cold before we realised that the truth was the opposite).

Can we see the acoustic peaks in the CMB?

Humanity's measurement of the fluctuations in the temperature of the CMB is certainly a remarkable technical achievement. However the mere existence of these fluctuations doesn't tell us all that much. In reality, almost anything could have caused small fluctuations to exist in the CMB. But! if these temperature fluctuations really did come from density fluctuations in the (now well discussed) primordial hydrogen plasma, we should be able to see some acoustic peaks hiding somewhere in this photograph.

And we can!

Loosely speaking (I've run out of space again), we can find them in the following way. Firstly, we break the whole sky up into many smaller pieces that each have the same size. We then observe the CMB in each of these pieces. Any particular choice for the size of these sky pieces will correspond to a particular size for the region of the primordial universe that generated the part of the CMB that is observed. We can then measure the average temperature fluctuation in the CMB in each of these sky pieces and equate it to the average temperature fluctuation in the corresponding region of the primordial universe. If all goes to plan we should expect to be able to see acoustic peaks if we plot the amplitude of the average temperature fluctuations in the sky against the sky piece size.

The figure below is more or less this exact plot. That big peak in the figure is the first acoustic peak described above. You can see clearly that the sound horizon takes up about one degree on the sky. There are also other peaks in this plot. They correspond to region sizes in the early universe that have had time for one full pulsation, or one and a half. The actual measurement in this plot is the set of black and coloured data points (black from WMAP, coloured from ground and balloon experiments). The red line/band is the best fit that the standard cosmological model can make to this data.

So... the acoustic peaks exist! That is, the photograph we have taken today of some very cold light that happens to be permeating all of space really does record the effects of extraordinarily quiet sound waves that rippled through the universe 13.7 billion years ago! Incredible!

Through analysing this image we are able to extract information about the primordial density fluctuations that existed in the hydrogen plasma at the very dawn of the Big Bang. We are also able to extract information about the density of dark matter in the universe. This is because it is dark matter that provides the gravitational wells for the hydrogen plasma to fall in and out of as it pulsates for 400,000 years. We can use this image to extract information about the curvature of the space that the CMB travels through for those 13 or so billion years. A curvature of space bends the path of the CMB which causes the locations of the acoustic peaks in the sky to differ. We can even use this image to extract some information about the rate at which the universe expands. If the universe has expanded slightly more than we expect, then the CMB we are measuring has come from further away. This would also change the location of the acoustic peaks in the sky.

Think back to my analogy of the two buildings and the fact that the CMB was made billions of years ago to remind yourself just how hard it was to measure these fluctuations. This is why the measurement of the acoustic peaks in the CMB is one of the greatest feats of detective work... ever.

Taking the coffin to the graveyard, burying it and silently placing the tombstone on the grave...

I wrote at the beginning of this post that the detection of the acoustic peaks in the CMB temperature fluctuations represented the final nail in the coffin of all things not the Big Bang. This is true. However it turns out that the CMB is hiding still more information about the early universe. The sound waves in the primordial hydrogen plasma also induce a polarisation in the CMB. This polarisation is exceedingly (almost outrageously) small, but it is there and its correlation with the temperature anisotropies has now been measured. There is absolutely no reason to expect that a CMB that did not arise from an almost-but-not-quite-silent hydrogen plasma should have such a correlation, but yet again, it is there. Astounding!

Twitter: @just_shaun