Ask Ethan: How do we know the timeline of our Universe?

Today, it’s now 13.8 billion years since the Big Bang occurred. Our observable Universe extends for 46.1 billion light-years in all directions, and is made of:

• 68% dark energy,
• 27% dark matter,
• 4.9% normal (atom-based) matter,
• 0.09% neutrinos,
• and 0.01% radiation,

with no hint of other components like spatial curvature, cosmic strings, domain walls, or any other weird stuff we can imagine.

If we were to run the clock backward, however, we’d find that dark energy wasn’t always dominant. There was a time when matter dominated, and before that, when radiation did. There was a time when there were no stars, no neutral atoms, no atomic nuclei, no protons and neutrons, and even no massive particles.

But how do we know precisely when these events and epochs occurred? That’s what Marshall Randolph wants to know, asking:

“When I read about the epochs of the universe, they are tagged with a specific time. The Hadron epoch, for example, started at 10^-6 seconds. The timelines of the epochs are given almost as if I should know them. Are they easily calculated by physicists? Could you describe the methods in a way I can understand?”

I very much think so. Let’s recount the cosmic story of how we came to be and how we know precisely when those events happened.

The relative importance of different energy components in the Universe at various times in the past. Note that when dark energy reaches a number near 100% in the future, the energy density of the Universe (and, therefore, the expansion rate) will remain constant arbitrarily far ahead in time. Owing to dark energy, distant galaxies are already speeding up in their apparent recession speed from us. Way off the scale of this diagram, to the left, is when the inflationary epoch ended and the hot Big Bang began. Dark energy’s energy density is ~123 orders of magnitude lower than the theoretical expectation.

In the beginning — at least, as far back as we can trace things — the Universe was inflating. That means it was expanding relentlessly, doubling in scale in all directions with each tiny fraction-of-a-second (something like 10^-35 seconds) that goes by. After only a few hundred of those doublings, a tiny quantum fluctuation occurring on Planck scales, the smallest scale we can describe before the known laws of physics break down, gets stretched to scales even larger than the observable Universe. Because of this rapid expansion, the Universe quickly empties; the only thing in it is empty space, and the large amount of energy tied up in whatever quantum field caused inflation, plus the small amount of “fluctuation energy” arising from the stretched quantum fluctuations occurring on all scales.

Then inflation ends, and that field energy gets converted into all the quanta we know of. Particles and antiparticles of all types, including photons, get spontaneously created at very high energies and very large densities. They’re almost uniformly distributed, with an average “overdense” region and an average “underdense” region departing from the average density by just one part in ~30,000 or so. From this point on, the Universe always expands, cools, and gravitates, and all sorts of events in the evolutionary history of our Universe occurs.

How matter (top), radiation (middle), and dark energy (bottom) all evolve with time in an expanding Universe. As the Universe expands, the matter density dilutes, but the radiation also becomes cooler as its wavelengths get stretched to longer, less energetic states. Dark energy’s density, on the other hand, will truly remain constant if it behaves as is currently thought: as a form of energy intrinsic to space itself. These three components, together, dictate how the Universe expands at all times from the Big Bang until the present day and beyond.

At the start, these quanta all collide with one another at tremendous rates: quadrillions of times per second. They’re all massless, so they’re all moving at the speed of light, possessing very large amounts of energy. But as the Universe expands, it also cools: remember that all particles, massive or massless, can be described by a wave as well, and the wavelength of any wave determines its energy. As the Universe expands, the wavelength of all waves get stretched, meaning they lose energy and the temperature of the Universe drops.

At some point:

• the Universe cools enough so that the shortest-lived, most unstable particles and antiparticles begin decaying,
• the Higgs and electroweak symmetries break, giving rise to rest mass and separating the weak and electromagnetic forces,
• the quarks-and-antiquarks and gluons, previously free particles, become grouped into protons, neutrons, and other bound states known as hadrons,
• the antimatter annihilates away with most of the matter, creating a great bath of radiation and just a small population of excess matter,
• nuclear fusion can occur without composite nuclei immediately being blasted apart,
• matter overtakes radiation as the dominant component of the Universe,
• neutral atoms can stably form, giving rise to a Universe that’s now transparent to visible light,
• the first stars form, paving the way for the era of stars and galaxies,
• and then dark energy overtakes matter as the dominant component of the Universe, ensuring our cosmic fate to be driven away from all unbound galaxies and groups/clusters of galaxies.

That’s a very rough outline of the history of the Universe.

This artist’s conception shows a logarithmic view of the observable Universe. The Solar System gives way to the Milky Way, which gives way to nearby galaxies which then give way to the large-scale structure and the hot, dense plasma of the Big Bang at the outskirts. If we were to shrink the Sun down to a grain of sand, then the observable Universe would only be a little over a hundred billion kilometers in radius, containing around 2 sextillion “grains of sand” (stars) strewn across that enormous volume.

Now for the big question: how can we determine when all of these things happen?

The way we normally do this is straightforward — at least conceptually — even if the mathematics itself is a little difficult. Where we start is by recognizing the following three things:

1. The Universe presently has a “bath” of background radiation that’s left over from the Big Bang, with an average temperature, today, of 2.7255 K.
2. The Universe presently has a specific “size” or “scale” to it, which we believe is very close to 46.1 billion light-years in radius, but which we can just call “the size today.”
3. And that, because the Universe is continuously expanding and cooling, it was smaller and hotter and denser in the past, and we can determine “How hot was it?” at any point in time simply by recognizing that if you take the temperature today and divide it by the ratio of “the scale of the Universe back then” to “the scale of the Universe today,” you’ll get the temperature of the Universe back at any epoch you desire.

Therefore, if you know either:

• what was the temperature/energy at which this specific event-or-transition occurred,
• or what was the scale, relative to today’s scale, at which this specific event-or-transition occurred,

you can do the math to figure out precisely when, in terms of our cosmic history, these events and eras took place.

A visual history of the expanding Universe includes the hot, dense state known as the Big Bang and the growth and formation of structure subsequently. The full suite of data, including the observations of the light elements and the cosmic microwave background, leaves only the Big Bang as a valid explanation for all we see. As the Universe expands, it also cools, enabling ions, neutral atoms, and eventually molecules, gas clouds, stars, and finally galaxies to form. Without the Higgs giving mass to the particles in the Universe at a very early, hot stage, none of this would have been possible.

Figuring out either temperature/energy or relative scale at which certain events occurred is relatively straightforward. For events that occur in the context of particle/high-energy physics, we simply need to look to our experimental data to figure out at what energy/temperature they occur at. For events that occur throughout the history of the Universe, these can either be measured or calculated using one of two straightforward methods.

1. For events that can be determined observationally, we can measure the redshift at which they occur/exist, by comparing the observed emission/absorption lines generated by atomic or molecular transitions with the same lines generated that same molecule or atom within the lab. The ratio of observed-to-rest-frame wavelength equals the ratio of “the scale of the Universe back then” to “the scale of the Universe today,” and that ratio, minus the number 1, is the definition of redshift.
2. For events that can occurred at some point in the Universe’s past, we can calculate “What was the scale of the Universe back then?” simply by numerically integrating the equation that governs how the Universe expands over time: the first Friedmann equation.

A photo of Ethan Siegel at the American Astronomical Society’s hyperwall in 2017, along with the first Friedmann equation at right. The first Friedmann equation details the Hubble expansion rate squared on the left hand side, which governs the evolution of spacetime. The right side includes all the different forms of matter and energy, along with spatial curvature (in the final term), which determines how the Universe evolves in the future. This has been called the most important equation in all of cosmology and was derived by Friedmann in essentially its modern form back in 1922.

If you can figure out what the Universe’s scale factor was when a specific transition occurred, then you can do a little math to determine “At what time in the Universe’s history was the Universe this specific size/scale?” Again, this requires some numerical integration, but there’s a short-cut you can use that works pretty well for the first few billion years of our cosmic history: assuming the Universe was either made 100% out of radiation (which works for the first ~10,000 years), or assuming that the Universe was made 100% out of matter (which works for the next ~7 billion years).

The short-cut is as follows.

• If your Universe is made 100% of radiation, then it expands according to a simple rule: the scale factor grows with time as a ~ t^½.
• If your Universe is made 100% of matter, then it expands according to a simple rule: the scale factor grows with time as a ~ t^⅔.
• And if your Universe is made 100% of dark energy, which dominates the expansion at late (modern) times, the scale factor grows exponentially: as a ~ e^Ht.

If we fill in the in-between stages, or just calculate the whole thing directly without using short-cuts, we can determine the scale/size of the Universe as a function of cosmic time.

The scale of the Universe (y-axis) versus the age of the Universe (x-axis) on logarithmic scales. Some size and time milestones are marked, as appropriate. Everything contained within the entire observable Universe was once contained in a very small volume, as shown by the size scale on the y-axis.

That’s it, as long as you realize

• that the ratio of the scale of the Universe at any time to the scale of the Universe today

is equal to

• the temperature of the Universe at any time to the temperature of the Universe today,

you can calculate at what time any event occurs if you know either how big the Universe was at that time relative to today or you know what the temperature of the Universe was at that time relative to today.

With that said, all we need to remember is that the temperature of the Universe, today, is 2.725 K, and that the size/scale/redshift of the Universe today is 46.1 billion light-years/defined as 1/defined as 0, and also that the age of the Universe, today, is 13.8 billion years after the Big Bang. As long as you start with today’s composition of the Universe — 68% dark energy, 31.9% matter, 0.09% neutrinos and 0.01% photons — and you recognize that everything behaves as radiation when it moves at or very close to the speed of light, you can’t go wrong.

With that said, here is a summary of the various eras/epochs, from the earliest moments we can speak of until the present day.

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.

Inflationary era: This is a tricky one, but only in the sense that we don’t know when, how, or even if it had a beginning, but we do know that it lasted at least some ~10^-33 seconds, and that when it ended, the hot Big Bang began.

Free, unbound, massless particle-and-antiparticle era: This is what you might think of as the Universe’s “primordial soup,” where every possible collision that you can imagine occurs in great abundance. There are no bound structures; there are no stable configurations; any particle that you can track likely gets annihilated and transforms into other particles many, many times over. This lasts from the end of inflation right up until the Universe is about ~10^-10 seconds old, or ~100 picoseconds.

Massive particle-and-antiparticle/quark gluon plasma era: After about the first ~10^-10 seconds, the Higgs and electroweak symmetries break, separating the electroweak force into the electromagnetic and weak forces, and giving mass to the Universe. This transition is also the final opportunity for the Universe to create a matter-antimatter asymmetry; if it hasn’t happened before now, this is its last opportunity. As it expands and cools, the heavier quarks-and-antiquarks decay away, as do the tau-antitau lepton pairs. This continues until the Universe is about one microsecond (~10^-6 seconds) old, when the next major transition happens.

In the very early Universe, there were tremendous numbers of quarks, leptons, antiquarks, and antileptons of all species. After only a tiny fraction-of-a-second has elapsed since the hot Big Bang, most of these matter-antimatter pairs annihilate away, leaving a very tiny excess of matter over antimatter. How that excess came about is a puzzle known as baryogenesis, and is one of the greatest unsolved problems in modern physics.

Hadron era: Prior to this point, quarks-and-antiquarks and gluons were still in a primordial soup: the quarks-and-antiquarks had masses, but wouldn’t form bound states, as the energies and densities were too great. But now, groups of three quarks form baryons like protons and neutrons, groups of three antiquarks form anti-baryons, and quark-antiquark pairs form mesons. All of the mesons are unstable, and decay quite quickly, while the remaining anti-baryons all get annihilated away by baryons, producing an enormous bath of radiation. At the end, there are a whopping ~1 billion photons left over for every baryon, but no surviving antibaryons. This lasts until the Universe is about 1 second old, and a handy rule-of-thumb is that an age of ~1 second corresponds to an average energy-per-particle of 1 MeV, or a temperature of ~10¹⁰ K: ten billion degrees.

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Nuclear era: At an age of ~1 second, neutrinos stop interacting regularly with the remaining particles and antiparticles in the Universe, and almost immediately after, the remaining positrons annihilate with a huge excess of electrons, producing even greater numbers of photons, and heating them so they’re slightly hotter (by about 40%) than the neutrinos. Nuclear fusion is attempting to occur between protons and neutrons, but the photons blast them apart until the Universe reaches about ~3 minutes of age. At last, now that it’s cool enough, nuclear fusion occurs, forming deuterium, tritium, helium-3, helium-4, and both lithium-7 and beryllium-7. By the time the Universe is about 4-to-20 minutes old, all of this is done.

A Universe where electrons and protons are free and collide with photons, transitions to a neutral one that’s transparent to photons as the Universe expands and cools. Shown here is the ionized plasma (left) before the CMB is emitted, followed by the transition to a neutral Universe (right) that’s transparent to photons. It’s the spectacular two-photon transition in a hydrogen atom which enables the Universe to become neutral exactly as we observe it.

Plasma era: It’s now too cold and too sparse for fusion reactions to occur, and all of the tritium decays to helium-3 while all of the beryllium-7 decays to lithium-7. Protons and the other atomic nuclei would love to bind together to electrons, but they can’t without getting immediately blasted apart by a high-energy photon. At an age of about ~9,000 years, radiation quits being the dominant component of the Universe, replaced by the combination of normal-and-dark matter. This lasts until the Universe reaches an age of about 380,000 years, and a temperature of merely ~3000 K.

Atomic era: At last, at this point, 380,000 years after the Big Bang, the Universe forms neutral atoms, and is now transparent to light, including the radiation left over from the Big Bang. But because the densest overdense regions and the least-dense underdense regions are still so close to the cosmic average, it takes time for gravitation to collapse these atoms down to where they can form stars. Although the exact number isn’t yet known, we can ballpark it to last until the first stars form, say, 100 million years after the Big Bang.

Stellar-and-galactic era: Beginning roughly 100 million years after the Big Bang, now “Let there be light” has officially occurred for the second time: with the birth of stars and star clusters. These will grow and merge into galaxies, galaxy groups, and clusters, and will align along great cosmic walls, eventually forming the modern cosmic web.

Over time, gravitational interactions will turn a mostly uniform, equal-density Universe into one with large concentrations of matter and huge voids separating them. For as long as radiation is still important, exerting an outward pressure even once the Universe becomes matter-dominated, the growth of matter imperfections is very small.

Although this process persists far into the future, we’ve already entered the final one: the one that describes our Universe now and will describe our Universe for all-time afterward.

The dark energy era: There are two ways to define its onset, depending on whether you define “dark energy dominates the Universe” as talking about

• when the recession speed of a distant galaxy stops slowing down and starts speeding up,
• or when dark energy becomes the dominant form of energy in the Universe, overtaking matter.

By the first definition, dark energy dominates the expansion rate of the Universe at an age of 7.8 billion years after the Big Bang. By the second definition, that domination is delayed until the Universe is 10.4 billion years after the Big Bang. Right at the same time that the first photosynthetic organisms evolve on Earth, dark energy passes both dark matter and normal matter combined to dominate the energy content of the Universe.

And that’s the way it will be, forever and ever into the future, at least to the best of our knowledge. This timeline can be made more-or-less granular, but that’s how we know it and how we figure it out!

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