The most “boring” part of cosmic history shaped our modern Universe

It was 13.8 billion years ago that our Universe, as we know it, began: at the start of the hot Big Bang. After an initial period of cosmic inflation came to an end, the Universe became filled with particles and antiparticles of all different varieties at incredible temperatures, all while it remained expanding at a very rapid rate. Almost immediately, the Universe began cooling as it expanded, and the temperatures dropped precipitously. After only a trillionth of a second, things had cooled enough that the electroweak symmetry broke, creating four fundamental forces and allowing the Higgs to give rest mass to the Standard Model particles. In the aftermath of that:

• an early quark-gluon plasma condensed into individual baryons, such as protons and neutrons,
• the remaining antimatter annihilated away, leaving only a tiny amount of leftover normal matter,
• the weak interactions froze out, creating a background of cosmic neutrinos and antineutrinos,
• about 20% of the neutrons that existed decayed into protons while waiting for the Universe to cool sufficiently,
• so that nuclear fusion reactions could take place, creating the light elements in the early stages of the hot Big Bang,
• and then it cooled enough so that neutral atoms could eventually form.

It’s only after the formation of neutral atoms that our first directly observable signature from the Universe — the cosmic microwave background (CMB) — appears. But while all of those early events occur in the first few minutes of cosmic history (with most coming in the first fraction-of-a-second after the Big Bang), neutral atoms don’t form until a full 380,000 years have passed. And yet, it’s that “boring” time, after Big Bang nucleosynthesis ends but before neutral atoms form, that the backbone of cosmic structure in our modern Universe is formed. Here’s why that “boring” ~380,000 years is so important for today’s cosmos.

The quantum fluctuations inherent to space, stretched across the Universe during cosmic inflation, gave rise to the density fluctuations imprinted in the cosmic microwave background, which in turn gave rise to the stars, galaxies, and other large-scale structures in the Universe today. This is the best picture we have of how the entire Universe behaves, where inflation precedes and sets up the Big Bang. Unfortunately, we can only access the information contained inside our cosmic horizon, which is all part of the same fraction of one region where inflation ended some 13.8 billion years ago.

Back when the hot Big Bang first occurred, it was expanding, cooling, full of matter and radiation, and — importantly — almost perfectly uniform in temperature and density everywhere. The “almost” part is supremely important here, because if it were absolutely, perfectly uniform with no exceptions at all, then it would remain perfectly uniform at all times; there would be no structure that would wind up forming. Gravitation, remember, is an attractive force: wherever you have two masses, they attract each other. But if your Universe were perfectly uniform, then every mass would be pulled on equally in all directions by the other masses in the Universe, and no regions would “win out” in the end, leading to stars, galaxies, and larger-scale cosmic structure. If everything were perfectly uniform, no complex cosmic structures would ever appear.

But our Universe wasn’t born perfectly uniform, and the reason for that is simple, straightforward, and powerful: because inflation, which preceded and set up the hot Big Bang, provided the seeds of cosmic imperfections that would grow into the structures we observe today. The way inflation does this is by being a quantum field, because like all things quantum, it experiences brief fluctuations in energy owing to Heisenberg’s uncertainty principle. These field fluctuations get stretched to all scales during inflation, and when inflation ends, it creates an almost-perfectly uniform Universe, but with overdensities and underdensities present on all scales: at about the 1-part-in-30,000 level.

We can look arbitrarily far back in the Universe if our telescopes allow, and the clustering of galaxies should reveal a specific distance scale – the acoustic scale – that should evolve with time in a particular fashion, just as the acoustic “peaks and valleys” in the cosmic microwave background reveal this scale as well. The evolution of this scale, over time, is an early relic that reveals a low expansion rate of ~67 km/s/Mpc, and is consistent from CMB features to BAO features.

During the very early stages of the hot Big Bang, these fluctuations barely change at all. Those first few fractions-of-a-second, those next few minutes, or even those first few days, months, and years all have negligible effects on these fluctuations. They remain slightly overdense and slightly underdense regions of space, just as when they were created. But as time continues to pass, even before the formation of neutral atoms, gravity is still present, doing exactly what it does: causing spacetime to curve, expand, and evolve based on the distribution of matter and energy within it, while the matter and energy within it respond to the curvature of spacetime by moving, as compelled by the force of gravity.

This means that the overdense regions — the regions of space with more matter than average within them — begin preferentially attracting surrounding matter towards them, by slightly greater amounts than the regions of average or below-average density. Similarly, the underdense regions, by virtue of having less matter than average within them, begin preferentially giving up their matter to the surrounding, denser regions. If all we had in the Universe was matter, this would be the process by which structure would form: the “rich” regions would get richer in matter, while the “poor” regions would get poorer in matter. It would be a runaway process.

This snippet from a structure-formation simulation, with the expansion of the Universe scaled out, represents billions of years of gravitational growth in a dark matter-rich Universe. Over time, overdense clumps of matter grow richer and more massive, growing into galaxies, groups, and clusters of galaxies, while the less dense regions than average preferentially give up their matter to the denser surrounding areas. The “void” regions between the bound structures continue to expand, but the structures themselves do not.

Only, in these early stages of cosmic history, we have a lot more than matter that’s important. For starters, we have two types of matter early on:

• normal matter, which is made of protons, neutrons, and electrons, and which interacts with (i.e., absorbs, emits, and scatters off of) photons,
• and dark matter, which doesn’t interact with normal matter or photons at all.

Then, on top of that, we also have another ingredient: radiation, or the leftover bath of (very hot) photons, as well. This paints a much more accurate, albeit more complicated, picture of what the “late, early Universe” was like: after Big Bang nucleosynthesis, but before the formation of neutral atoms.

So what happens, then, after Big Bang nucleosynthesis ends, when we don’t yet have neutral atoms?

The first thing that happens is exactly what we would have expected:

• the overdense regions preferentially attract the matter from their (relatively less dense) surroundings,
• while the underdense regions preferentially give up their matter to their (relatively denser) surroundings,

so long as the “scale” of those regions is smaller than the current cosmic horizon, or the length scale that any signal — including a gravitational one — could have traveled since the start of the hot Big Bang. Initially, the overdense regions, so long as they’re on a small enough cosmic scale (relative to the time elapsed since the start of the hot Big Bang), will begin to gravitationally grow, becoming more dense. (Similarly, the initially underdense regions start to get less dense.)

Regions of space that are slightly denser than average will create larger gravitational potential wells to climb out of, meaning the light arising from those regions appears colder by the time it arrives at our eyes. Vice versa, underdense regions will look like hot spots, while regions with perfectly average density will have perfectly average temperatures.

But then, something else happens as a consequence of these changes in density. As the overdense regions gets more and more dense, the radiation that’s present within them (in the form of photons) preferentially streams out of those regions. This reduces the overall energy density of those regions, while increasing the outward pressure due to radiation: pressure that can push normal matter (but not dark matter) out of them.

In other words, there’s a limit to how dense an overdense region is going to get under these conditions. Sure, gravity will cause these overdense regions to grow, but the fact that there’s also large amounts (in terms of energy) of radiation present means that:

• as the overdense regions get denser,
• the radiation pressure inside those regions rises,
• causing radiation to stream out of them,
• pushing on the normal matter (more than the dark matter),
• leading to the the density in those regions eventually dropping,
• which causes them to be less attractive,
• and, therefore, to stop gravitationally growing.

Of course, this can only happen once the scale of the cosmic horizon is large enough for a density fluctuation on those specific scales to begin growing, while the exact opposite process happens for the underdense regions.

The fluctuations in the cosmic microwave background, as measured by COBE (on large scales), WMAP (on intermediate scales), and Planck (on small scales), are all consistent with not only arising from a (slightly tilted, but almost-perfectly) scale-invariant set of quantum fluctuations, but of being so low in magnitude that they could not possibly have arisen from an arbitrarily hot, dense state. The horizontal line represents the initial spectrum of fluctuations (from inflation), while the wiggly one represents how gravity and radiation/matter interactions have shaped the expanding Universe in the early stages.

This means that, for small cosmic scales (scales smaller than the cosmic horizon at even early times), the overdense regions will begin growing, but will only grow to some maximum size, and will then shrink again. If we watched this region under these conditions for a long enough period of time, we would see the “amount of overdensity” present begin to oscillate: growing and shrinking and growing and shrinking periodically, as radiation and matter flow into and out of these regions.

But if we went to a slightly larger set of cosmic scales, we would see the same thing happen, but it would take greater and greater amounts of time for these steps to occur. Remember: gravitational growth (or, for underdensities, gravitational shrinkage) can only begin when the scale of the cosmic horizon exceeds the scale of the initial overdensity. As the Universe ages, it expands, but the scale of the cosmic horizon (or the speed at which a signal can reach) grows faster than the expansion of space on these relatively small cosmic scales.

This means that, over time, the initially smaller-scale regions start oscillating after initially growing, but that initially larger-scale regions take longer to begin growing, and then, to begin oscillating as well.

At early times (left), photons scatter off of electrons and are high-enough in energy to knock any atoms back into an ionized state. Once the Universe cools enough, and is devoid of such high-energy photons (right), they cannot interact with the neutral atoms, and instead simply free-stream, since they have the wrong wavelength to excite these atoms to a higher energy level.

Finally, something begins to change. When the Universe achieves an age of around 300,000 years, the average photon temperature has dropped so sufficiently that now, at last, neutral atoms finally begin to form. When neutral atoms do form, now the composition of the Universe begins to change: instead of normal matter being made of atomic nuclei (protons and neutrons) and free electrons, some of it is now made of neutral atoms instead. Unlike ionized normal matter, which has a large interaction cross-section with photons, neutral atoms are mostly transparent to photons, and so there’s no more “pushing them back out” once they become neutral.

Although the process of forming neutral atoms takes a long time — more than 100,000 years, from start to finish — the average amount of time it takes for neutral atoms to form, after the start of the hot Big Bang, works out to more like 380,000 years. This corresponds to a time where the Universe was just 0.092% of its present size: more than a factor of 1000 smaller, in each of the three dimensions of space that we have (and, hence, more than a factor of a billion denser), than it is today.

At that moment in cosmic history, overdense regions that had scales of about ~460,000 light-years, from center-to-edge, had grown the most. These correspond to regions that had started gravitationally growing because they were smaller than the cosmic horizon at the time, but that hadn’t yet begun oscillating due to radiation streaming out of that region and/or pushing the matter back out.

Although we can measure the temperature variations all across the sky, on all angular scales, it’s the peaks and valleys in the temperature fluctuations that teach us about the ratio of normal matter to dark matter, as well as the length/size of the acoustic scale, where normal matter (but not dark matter) gets “bounced” outward from interactions with radiation. This radiation includes photons, which have a substantial cross-section with particles in the ionized plasma of the early Universe, and neutrinos, which do not.

That scale — of where matter has achieved the greatest overdensities relative to the initial amount of overdensity — is very special here in our late-time Universe. Sure, it shows up, as you see above, as the largest “peak” in the leftover glow from the Big Bang: the cosmic microwave background. But it winds up having a downstream effect that you might not have expected. After neutral atoms do form, this scale, as well as all smaller scales, are well within the cosmic horizon. As a result, they can now do what you would have initially expected an overdense region within an expanding Universe would do: gravitationally grow, unfettered by any other species of matter or radiation.

Because this specific scale, of ~460,000 light-years back when the Universe was just 380,000 years old, gravitational growth happens preferentially on this particular distance scale. What this means is that, when galaxies form, if you put your “finger” down on any one random galaxy within the Universe, it’s going to be more likely, statistically, that you’ll find another galaxy located that specific distance away — 460,000 light-years, multiplied by however much the Universe has expanded by — than by either a great or smaller distance.

This scale is known as the “acoustic scale,” and if you’ve ever heard the term baryon acoustic oscillations (or BAO) before, this is precisely what it’s referring to.

Standard candles (left) and standard rulers (right) are two different techniques astronomers used to measure the expansion of space at various times/distances in the past. Based on how quantities like luminosity or angular size change with distance, we can infer the expansion history of the Universe. Standard candles involve looking at objects whose intrinsic brightness is known at all cosmic distances, while standard rulers involve looking at features such as the average separation distance between any two galaxies (imprinted from baryon acoustic oscillations during the early stages of the Big Bang) that evolves as the Universe expands.

We often talk about “standard candles” in cosmology, which is the idea that you can measure some properties of an object that are (relatively) easily observable while simultaneously knowing/learning something about its intrinsic brightness. Then, when you measure its apparent brightness, you can automatically know how far away it is from you, just like if you knew how intrinsically bright a candle was, you could report how far away it was solely based on the brightness you observe. At the present time, type Ia supernovae are considered the “best” standard candle, because their intrinsic brightnesses can be well-understood, so when you measure their apparent brightness (and they are extremely bright), you can automatically know how distant they are.

However, baryon acoustic oscillations give us a different way to measure the Universe: with a standard ruler, rather than a standard candle. Because we know what the acoustic scale was at the moment that neutral atoms first formed, and we can measure (and calculate) how the Universe has subsequently expanded in all the time since, we can use galaxy clustering as a complementary probe of our Universe’s history, expansion, and composition. In fact, the brand new SphereX mission, along with ESA’s Euclid, NSF’s Vera Rubin observatory, and NASA’s already-built (and awaiting launch) Nancy Roman telescope, will measure these baryon acoustic oscillations across cosmic time better than ever before.

In the aftermath of inflation, signatures are imprinted onto the Universe that are unmistakably inflationary in origin. While the CMB provides an early-time “snapshot” of these features, that’s just one moment in history. By probing the large variety of times/distances accessible to us throughout cosmic time, such as with large-scale structure, we can obtain information that would otherwise be obscure from any single snapshot.

It’s a remarkable piece of information about our Universe: the fact that we have a “feature” imprinted on it from before we can even directly observe anything — including what created it — at all. However, just by understanding some basic facts about and ingredients within our expanding Universe, we can predict a series of acoustic peaks (and valleys) that are created within the primordial plasma early on in cosmic history: after Big Bang nucleosynthesis has completed but before the formation of neutral atoms. While many think of this as a “boring” time in cosmic history, because it lacks any of the important dramatic transitions that occurred earlier (or much, much later) during the hot Big Bang, it’s an important epoch for creating an imprint that will affect the rest of the Universe for all the time to come.

When you look at the modern, galaxy-rich Universe today, you’re seeing it as it is now: with galaxies, galaxy groups and clusters, and a large-scale cosmic web that has been shaped by gravity and cosmic expansion over billions of years. However, these signals from within the primordial plasma, created long before the very first star (or even the very first neutral atom!) could form, have left an imprint in our Universe that can be seen in both the cosmic microwave background and the clustering of galaxies, even today. Our modern Universe, in a great many fashions, truly is shaped by what happened in a cosmic blink-of-an-eye. If we truly care about what things are like today, in full detail, even the most “boring” parts of cosmic history have profound lessons to teach us.