Sound Waves from the Beginning of Time (Script) (Patreon)

Invisible to the naked eye, our night sky is scattered with the 100s of billions of galaxies the fill the known universe. Like the stars, these galaxies form constellations – hidden patterns that echo the reverberations of matter and light in an epoch long before galaxies ever formed. These are  the baryon acoustic oscillations, and they may hold the key to understanding the nature of dark energy.

The field of cosmology – the study of the universe on its largest scales – was once the least precise in all of astrophysics. The impossibly vast distances made accurate measurements near impossible. But as our telescopes and our techniques improved over the past few decades, things are now different. We live in the era of precision cosmology, in which we know to stunning detail the properties that govern the very birth, evolution, and end of our universe. We talked about one of those properties in a recent episode – the Hubble constant – and about a growing conflict in its measured value which hints at strange new physics. Today we’ll talk about another measurement that may help resolve this crisis: the baryon acoustic oscillations. They the fossils of the first sound waves in the universe, imprinted in the distribution of galaxies on the sky. And in these patterns we can read the expansion history of the universe.

Let’s start at the beginning. For the first few hundred thousand years in the life our universe, all of space was filled with hydrogen and helium in plasma form: protons and the lightest of nuclei forged in the first minutes after the big bang, and still so hot that no atoms could form and electrons buzzed free of their nuclei. These particles of matter are our baryons. There was also light. In fact, around a billion photons for every electron. But no photon is safe from a free electron! Unbound electrons present a huge target to scatter any wavelength of light – and scatter they did, constantly. A photon could barely travel any distance before colliding with an electron. The electrons in turn exerted their electromagnetic pull on the nuclei. We say that in this state, light was coupled with matter, and baryons and photons formed a single strange fluid – a baryon-photon plasma.

There are three profound differences between the behavior of matter in this state compared to the gentle gas nebulae of the modern universe. First, the baryon-photon plasma was opaque; there exist no lines of sight to anything during this time. We’ll come back to that. Second: light was able to exert an enormous of pressure on the plasma. As we’ll see, that will lead to the production of colossal sound waves. And third: those sound waves traveled fast. Rapid interaction between the charged particles of the plasma via the trapped photons meant that ripples in the plasma traveled at over half the speed of light.

Mixed with this soup of baryons and photons was also the dark matter. In fact dark matter outweighs baryons by a factor of 5, which means it was by far the dominant gravitational influence in the early universe, as it still is. But unlike baryons, dark matter does not interact with light at all. Light exerts no pressure on it.

OK, so the universe is filled with hot ocean of baryons, photons and dark matter. In order for it to do anything interesting we need one final ingredient: density fluctuations. A teensy bit more matter here, a teensy bit less there. These fluctuations were probably remnants of random quantum fluctuations from the when the universe was subatomic in size, and were expanded enormously by cosmic inflation in the beginning instant of the Big Bang. Immediately, two competing forces began to work. Each over-dense region pulled gravitationally on its surroundings, drawing matter towards it – in particular the dark matter flowed inwards towards the density peak. But also at that density peak

the imprisoned photons exerted an enormous outward pressure. 

To equalize this pressure, radiation pushed outwards and carried the baryons with it. This resulted in an acoustic wave – a true sound wave in the form of an expanding shell of increased density. And remember, sound traveled at over half the speed of light back then, so the shell expanded fast. But as it expanded so did the universe. As matter became more diffuse and the photons themselves were stretched – redshifted to lower energies – the universe cooled. At 380,000 years the plasma hit a critical temperature of 3000 Kelvin – around the surface temperature of the coolest red-dwarf stars. At this temperature electrons could finally be captured by nuclei and the first true atoms formed. The baryons transitioned in phase from a plasma to a gas. We call this phase transition event “recombination”.

While free electrons are able to interact with any frequency of light, electrons bound into atoms are restricted to only those specific frequencies corresponding to the energy level transitions of that atom. As a result, light and matter were no longer coupled – the universe went from opaque to transparent over a period of several thousand years. As the wave of plasma and photons decoupled; the light began to stream freely through the universe as the cosmic background radiation. But the plasma – now hydrogen and helium gas – stalled. The speed of sound dropped from half the speed of light to only hundreds of meters per second. The wave of plasma-turned-gas essentially froze in its current state. The radius of that shell became fixed to the rate of expansion of the universe. And its size? The exact distance that sound could travel over the age of the universe at that time. We call this the sound horizon, and at recombination it was around 500 thousand light years.

While all this was happening dark matter was doing its own thing. Immune to radiation pressure, the central dark matter over-density had continued to grow. It pulled on the expanding shell, and was pulled by it. When the expanding wave froze, both dark matter and baryons flowed together and consolidated the new structure. Once more in the gravitational grip of dark matter, hydrogen and helium could begin the long work of collapsing into stars and galaxies as the universe continued to expand. And now, over 13 and a half billion years later the universe has expanded by a factor of 1100. So those rings should be 150 Megaparsecs across, 500 million light years.

So how does all this primordial history lesson help us understand the subsequent expansion of the universe? Crazily we can still see those rings – not made of plasma or gas, but of galaxies. But before I show you what they look like, a note of caution. The story I just told about the early development of these density fluctuations is far from the whole picture. In reality, the density waves sloshed inwards and outwards, gravity pitted against radiation pressure. Density everywhere oscillated, with the rate of oscillation depending on the size of the initial fluctuation. Those are the oscillations in baryon acoustic oscillations, and the complex signature of that sloshing is imprinted in detail on the temperature map of the cosmic microwave background radiation. That’s something we’ll explore in a follow-up episode because it’s perhaps the most powerful tool we have in cosmology. But today we’re going to focus on this first this outbound density pulse, and how we see it in the arrangement of the galaxies.

So the acoustic shells at recombination overlapped in a complex web. Those rings were further smeared out over the thousands of years it took for the universe to fully transition from plasma to gas.  Collapse that web into galaxies over the age of the universe and at first glance it looks like a random smattering of galaxies on the sky. But the pattern is there. Detecting it required the most detailed surveys of the heavens ever conducted. It required galaxy redshift surveys. Redshift tells us the amount by which a galaxy’s light has been stretched as it traveled through the expanding universe. The more stretching the longer that light has traveled, and so the more distant it must be. Redshift gives distance, and with careful measurements of galaxies’ positions on the sky, a redshift survey can produce a 3-dimensional atlas of the universe.

With a galaxy redshift survey in hand, how do you find patterns in what looks like a random splattering of 10s to 100s of thousand galaxies? Well you expect that galaxies should mostly form in the centers of the primordial density fluctuations where the dark matter was the most concentrated. But you should also have a slight over-abundance of galaxies at exactly 150 Mpc from those clusters, corresponding to the acoustic rings. Everything is so hopelessly overlapping, but here’s what you do: in your atlas of the universe, take slices of the universe, each slice a certain distance from us. Within that slice, tally up the distances on the sky between every pair of galaxies. You should see a lot of galaxies that are close together – that’s the clustering from the giant dark matter density peaks. But you also see a slight excess of galaxy pairs with separations of 150 Mpcs. These are galaxy pairs where one is at the center of the dark matter peak and one is on the surrounding ring. That bump seems small, but it’s statistically very significant. It’s also exactly where we expected it to be.

The baryon acoustic oscillation signal was first spotted in 2005 by the Sloan Digital Sky Survey in the northern hemisphere galaxies and the 2dF survey in the south. Since then, the WiggleZ, BOSS, and 6dF surveys have improved the measurements. There was a powerful driving motivation to make this measurement. It was to confirm dark energy. Dark energy was first discovered by using distant supernovae as distance measures to track the rate of expansion of the universe. Those observations revealed that the expansion rate is accelerating due to an unknown influence that we call dark energy.

But such an incredible claim requires independent checking. They require an independent test of the expansion history. Enter baryon acoustic oscillations.  See, we know exactly how big those acoustic rings should be. Our understanding of the behavior of the original baryon-photon plasma is excellent. So we know how far the acoustic wave should have traveled, and we can confirm that prediction by looking at patterns in the cosmic microwave background. So we know how big those rings were when they formed, and we see how big they are at different points in the more modern universe from our redshift surveys. These rings give us a standard ruler on the sky, spanning all of cosmic time. They allow us to track the expansion rate of the universe.

The baryon acoustic oscillations agree with and confirm what we measured using supernova distances: the expansion of the universe is accelerating.  They confirm the existence of dark energy. Frankly, dark energy aside, just being able to see this pattern is cool enough for me. I mean, think about it - there are rings on the sky inscribed in galaxies, frozen echoes of the very first sound waves to reverberate across space time.