The Universe in a Box (Part 3): An Incredibly Brief History of Time

(This is Part 3 of a series of posts, introducing some of the major concepts in cosmology using a “cosmic cube”. Part 1 introduced the box, and described the expansion of the universe in that context; Part 2 went into some detail about the contents of the universe, including dark energy, the reason for the 2011 Nobel Prize in physics.)

To summarize the previous parts, rather than talking about the universe as a whole or even the entire observable universe (since we know we can’t see the whole thing, whatever “the whole thing” even means), we found it useful to introduce a cube several million light-years across. We found that this cube contains a microcosm of the entire universe, if something that big can be said to be “micro”: it has all the contents found in the cosmos in the same proportions, and it grows at the rate the entire universe grows. The stuff inside the box—ordinary matter, dark matter, light, and dark energy—affect how the box grows, and the box itself has an effect back on the contents. In the case of matter and light, a growing box dilutes the energy, making expansion slow down; in the case of dark energy, the increased size of the box means there is more energy inside the cube, driving expansion faster.

Now we are in a position to talk about how the universe has changed in time. The amount of matter (both ordinary and dark) is fairly constant over time, since creating or destroying matter is a high-energy process requiring high concentrations. This means the density of matter (amount of matter divided by the volume of the box) and of light (energy of all the photons divided by the volume) are smaller than it was in the past, and larger than it will be in the future. Running the clock backward, we find that the density of matter was really huge in the distant past when the cosmic box was smaller; similarly photons were not only more dense, but more energetic.

I didn’t talk much about neutrinos and other relativistic matter in part 2, but it’s worth sparing a few more words on them now. Neutrinos move at speeds close to light (leaving aside the OPERA results for now), so they don’t clump up like non-relativistic matter. This means they disperse like photons, but because they have mass, their energy behaves more like ordinary matter. In the early universe when the cosmic box was small, they influenced expansion in a significant way, but as with light, that influence waned quickly, so that we didn’t need to worry about them in our earlier discussion.

So, let’s list everything again:

  • Non-relativistic matter (including ordinary matter and dark matter) is slow-moving and can clump up. In the early universe, it was packed together, but its density drops as the cosmic box expands. We expect when density was high that its energy should be the dominant factor in the expansion of the cosmic box.
  • Relativistic matter (including neutrinos) doesn’t clump up, so it’s importance in terms of expansion will be large at first, but less and less significant as time passes.
  • Light also doesn’t clump, and because its energy depends on wavelength as well as the density of photons, as the universe expands, its influence will drop even more quickly than matter’s. However, that means it was even more significant in the past, because its wavelength was shorter when the cosmic box was small. We expect at very early times, therefore, that light will be even more dominant than matter, even though its role in today’s cosmic box is small.
  • Dark energy doesn’t seem to clump, and because of its weird behavior, in the early universe it effectively plays no part in cosmic expansion. However, because its density appears to be constant over time, there will be more of it in the future than there is today, so in the future it will dominate even more than it does now.

So here we go: a brief(er) history of time, not going all the way back to the beginning, but close enough for now….

From the Big Bang to Infinity, and Beyond

In the very early universe, our cosmic box picture breaks down: running the clock back until all the boxes were compressed together brings us to the Big Bang itself. We don’t have a good idea of exactly what was going on then: the four fundamental forces of nature were unified, but we don’t have a theory of exactly how. (Blah blah string theory blah.) If you trace the cosmic boxes backward in time that far, they won’t be the same size or shape: they won’t even be cubical boxes with flat sides! Everything inside each box would be a frothy mess, without the nice homogeneity and isotropy I discussed in Part 1: no galaxies, no stars, and this early in time, not even atoms or atomic nuclei.

Something really interesting happened in a tiny fraction of a second (about 10-34 seconds: a decimal place followed by 33 zeros and a one) after the Big Bang: a quantum fluctuation caused the universe to expand really rapidly, smoothing out all the inhomogeneities and flattening out all the differences between the cosmic boxes. (Events this close to the Big Bang happen really quickly, so hold on tight.) This event is called inflation, and while the details aren’t settled, the big picture is clear: without inflation, it’s hard to explain why our cosmic box picture works at all! The universe for much of its history is too smooth, too neat. Before inflation, it wasn’t homogeneous or isotropic; after inflation, it was.

Before inflation, the cosmic boxes weren't cubical or the same size. Inflation pumped energy into each box, smoothing out the differences and making them flat-sided and uniform. The actual amount of growth is much much much much larger than what I've shown here: each cell in the "Before" image should become 1042 times bigger in the "After" picture!

In the first three minutes after the Big Bang, most of the hydrogen, helium, and lithium in the universe formed, but it was still too hot to make stable atoms—the combination of nuclei with electrons. After inflation, in fact, the universe entered the radiation-domination epoch: high-energy photons kept the hydrogen and helium ionized, and their energy drove the expansion of the cosmos. Peering into the cosmic box during this era, everything would be bright, but opaque: the density of matter and radiation was high enough that photons couldn’t travel very far without hitting something.

Remember, though, that as expansion continues, photons lose energy density faster than matter. About 72,000 years after the Big Bang, the universe switched from radiation-domination to matter-domination, though it continued to be opaque. (That may sound like a long time in human terms, but remember that the universe is 13.7 billion years old: 72,000 years is about 0.0005% of the total age!) As we found earlier, when matter is dominant, the cosmic box expands, but its rate of expansion slows, so we see deceleration during this epoch.

During all this time, the universe is cooling down as photons lose energy and matter becomes less compressed. About 380,000 years after the Big Bang, the universe became transparent, and stable atoms were able to form for the first time. This flooded the universe with free photons in the ultraviolet part of the spectrum, but as the universe continued to expand, they redshifted into microwave wavelengths and are known today as the Cosmic Microwave Background (CMB). The CMB deserves at least one post to itself, so I’ll leave its details to another day.

The expansion of the cosmic box from the inflationary epoch through today. Sizes in both space and time are not to scale.

After the universe turned transparent, it was still filled with bright hot gas; the first stars formed about 200 million years after the Big Bang. Sometime in that period, the first galaxies also formed, and the cosmic box gradually began to resemble what we see today. Matter still dominated expansion, but since the box was growing, the amount of dark energy it contained was getting large enough to affect expansion. At a point around 4.2 billion years after the Big Bang, the balance tipped in favor of dark energy, which has been ascendant ever since, with accelerated expansion being the rule of the day. The figure shows the timeline of the universe (not to scale) from inflation down to today.

The contents of the universe today, and 380,000 years after the Big Bang. (Image from the WMAP website.)

I’ve noted that the total amount of matter in the universe and the total number of photons are roughly the same over long periods of time. The difference in what dominates expansion has to do with its density as well as its energy. Taking this into account, we see that at the time the Cosmic Microwave Background formed, dark matter, atoms, and neutrinos—all types of matter—together comprised 85% of the energy content of the cosmic box, with photons making up the remaining 15%. Dark energy is there, but it makes up far less than 1% and is invisible. Today, photons’ influence is gone and matter has waned to about 28% of the energy content of the cosmic box, with only about 5% of that being ordinary matter.

What of the future? If things continue as they are, dark energy will only continue to grow in influence, until a pie graph of the contents of the cosmic box will be almost entirely dark energy, with just a slim line representing everything else. The future of the universe is empty and dark, with the distances between galaxies growing ever larger. It will be long time, though, before the universe looks a lot different than it does today, so astronomy as we practice it won’t become obsolete until long after our own Sun dies out in 5 billion years.

This was indeed a very brief history. I haven’t done justice to inflation or the Cosmic Microwave Background, and have only begun to discuss the galaxies and galaxy clusters inside a given cosmic box. Part 4 of this series will examine structure formation: why the inside of the box looks the way it does today; Part 5 will look at the details of how inflation molded the a messy chaotic early universe into something describable using the cosmic box metaphor.


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