In this section, we look at how primordial sound is generated, and why its sound spectrum has the semi-musical form that it does.
The origin of primordial sound is quite a puzzle. This may seem odd given the (in)famous title "The Big Bang". But this title wasn't coined with sound in mind; instead it was first used by Fred Hoyle during a BBC series in 1950 to gently ridicule what was, to him, an unappealing theory. The title does evoke, however, an explosive origin, which one might understandably assume, as with all terrestrial explosions, was accompanied by a big "BANG".
Not so. The bizarre truth is that the Big Bang started out utterly silent! The initial expansion was absolutely pure and "radial" - no parts were catching up any other parts, and hence there were no pressure waves, and hence no sound. All was quiet.
So how did sound get started? Fortunately for us, although the expansion itself was smooth, the distribution of matter and energy was not. From the earliest moments, different regions of the Universe had very slightly different densities. The origin of these variations is a deep and fascinating story, which is unfairly boiled down to: quantum fluctuations at the first instant were amplified to significance by a brief period of inflation, and continued growing with the expansion. We'll return to this initial roughness, but for now all we need to know is that from the start, pervasive density variations create gravitational "hills" and "valleys" which pull on all matter.
As time goes by, responding to these pulls, gas begins to move — it begins to fall away from the hills and into the valleys. Follow its progress on the figure:
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One of the most surprising aspects of the CMB sound spectrum is all those bumps and wiggles - the fundamental and harmonics. Why should the Universe have these different "modes of vibration"? For everyday objects, the fundamental comes from a mode of vibration in which a single wave (twist or bend) crosses the object, while harmonics arise when two, three, four... waves cross the object, taking roughly (sometimes exactly) half, third, quarter... of the time. Since the Universe isn't a finite structure the reason for its fundamental and harmonics is a little different.
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This great diagram from Charlie Lineweaver shows how they come about. Remember, cosmic sounds arise from gas falling into a gravitational "valley" (a region of higher density) and then bouncing out again. Well, it takes time for the gas to do this and, not surprisingly, it takes longer for gas to fall into, and rebound out of, larger valleys. Now consider the CMB; it shows the Universe 400,000 years after the Big Bang. At this time, there is a biggest valley where the gas has only just arrived at the bottom for the first time – it is fully compressed, maximally bright, and these biggest valleys make the biggest patches on the CMB — they are the fundamental. Bigger waves simply don't exist yet; there hasn't been enough time for them to form.
How big is the fundamental wave/valley? Easy; how far do compression waves, moving at the speed of sound, travel in 400,000 years? For reasons we'll get to, sound and light had similar speeds, and we find these giant waves, which provide the deepest tones to the primordial sound, are 220,000 light years across.
Having described the origin of the fundamental tone, two further aspects of the CMB sound spectrum nicely fall into place: the origin of harmonics; and their blurring by "Doppler Distortion".
While the fundamental arises from the biggest valleys, what about smaller valleys? It takes less time for gas to fall into these, so after 400,000 years several oscillations might have occurred. Specifically, there is a sequence of ever smaller valleys where the gas has just arrived back at the valley floor for the second, third, fourth... times, adding patchiness to the CMB which generates the 3rd, 5th, 7th harmonic peaks (counting the fundamental as 1st). These odd numbered harmonics are called "compression peaks" because they come from gas being compressed at the valley floor.
You've probably guessed how the even peaks arise: they come from a sequence of ever smaller valleys where the gas has just rebounded out for the first, second, third times, giving rarefaction at the valley floors, leading to CMB patchiness which generates the 2nd, 4th, 6th harmonics. These are called, not surprisingly, "rarefaction peaks". You can follow all this on the previous figure.
You can also see how valleys of intermediate size are caught with gas moving from valley to peak. In these valleys, the gas is neither compressed nor rarefied, but its Doppler shift adds power between the harmonics, blurring them.
At this point in the story, it is worth bringing light into the picture since, if we are honest, a more accurate name for creation would be the Big Flash, not the Big Bang.
We are told from high-school never to confuse sound and light. Today, they behave so differently in part because we live in a world where matter's mass dominates utterly, and light's role is relegated to a feeble, though fleet footed, messenger. In the early Universe, the roles of matter and light were reversed, and light ruled with Herculean power — matter, so to speak, was a leaf in the wind. Later, we'll tell light's story more fully, but for now we'll note that photons – those evanescent particles of light – outnumbered protons or electrons by about a billion to one. The fog was a hugely bright, thin, low density fluid, in which light and matter were bound as one.
Because of light's enormous abundance at that time, the conditions within the fog were unlike anywhere here on Earth, or even inside stars – amazingly, the pressure exerted by light was a billion times greater than the pressure exerted by matter. This means that although the pressure waves were still, by definition, sound waves they were nevertheless pressure waves "in light" – great surges in the brightness of the fog, moving through the Universe. Matter did move back and forth as in normal sound, but it was pushed by light's pressure.
As you might imagine, since light's pressure is so high, and matter so sparse, the sound waves moved extremely fast: ~50% - 60% of light-speed, or ~150,000 km/s.