The Universe in a Box (Part 2): Opening the Box

(Part 2 of a growing series on basic cosmology concepts. Part 1 introduces the idea of the “cosmic box”, lays out some of the major contents of the universe, and describes expansion of the universe in terms of the box.)

A cosmic cube, with sides 500 million light-years long. Each face is part of the 2dF survey, so each yellow blob represents a real galaxy. With a cube this large, you can begin to see why cosmologists claim the universe is homogeneous: the cube is fairly uniformly yellow.

In Part 1, I introduced the idea of a cosmic box: an imaginary cube hundreds of millions of light-years across. Since we designed it to be huge, much bigger than any galaxy cluster, it will contain representatives of all the components the entire universe possesses — and in the same proportions. In addition, the changing size of the box reflects the expansion of the universe, so whatever is driving the expansion is contained inside the box.

So what is inside the box? Here are the basic categories:

  • Non-relativistic matter: stuff with mass that moves relatively slowly relative to cosmic expansion. This includes both ordinary matter (the building blocks of atoms, and so the raw material of stars, planets, life, and so forth) and dark matter (which is not made of any of the ordinary particles).
  • Relativistic matter: particles that move close to the speed of light relative to cosmic expansion. Neutrinos fall into this category.
  • Light: this one’s pretty obvious.
  • Dark energy, the name given to the stuff that drives the acceleration of the universe.

All of these things affect the expansion of the universe, but in different ways—which is partly how cosmologists determine the proportions of the various contents. (The other major way to determine the proportionality uses the cosmic microwave background (CMB); I will likely return to that in a later post.) Let’s consider the interplay between the box and its contents: how the changing size of the cube affects what’s inside it, and how the contents determine how the box grows.

Matter: Ordinary and Dark

Much of astrophysics is the interplay between the force of gravity, pulling matter together, and various types of pressure holding things from collapse into a black hole. Stars are spherical because gravity and gas pressure balance each other out; giant stars often deviate from being perfect spheres because gravity isn’t strong enough to hold the outer layers in against the pressure pushing outward.

The total amount of matter inside the box is constant, so as the box expands, the density of matter goes down dramatically.

Most of the ordinary non-relativistic matter inside our cosmic box is in the form of gas, and most of that gas is hydrogen. You might recall the ideal gas law from chemistry or physics class, which relates the pressure of a gas to its volume and temperature. A slightly more useful way to think about the gas law is in terms of the temperature and density of the gas: how many atoms or molecules are contained in a given volume. High pressure is the result of high temperatures and high density; inside our cosmic box, the average density of matter is pretty low compared even to the best vacuum we can make in the laboratory. The average temperature is also pretty low, even though there are regions where gases are heated to incandescence: the key again is in the huge size of the box. In other words, we can completely ignore the pressure from ordinary matter: it’s too small to make a different. (Stars, which are the other major container of ordinary matter, aren’t dense enough to generate pressure of this kind either; they will generate some pressure from their light, but as I mentioned in Part 1, the number of photons produced by stars is overwhelmed by the number from the cosmic microwave background.)

The best model we currently have for the stuff that isn’t ordinary matter is CDM: cold dark matter. “Cold” means it isn’t moving very quickly on average, indicating the particles of dark matter (whatever they are) must be fairly massive. Since dark matter doesn’t have an electric charge or magnetic properties, it doesn’t interact with light and hardly interacts with regular matter at all; “invisible matter” is more accurate than “dark”, which to me implies black in color as opposed to colorless. This means the pressure from dark matter has got to be tiny, too small to be important on the scale of our cosmic box.

If we can completely ignore pressure from both ordinary matter and dark matter, it’s not pressure making the cosmic box grow. Instead, according to Einstein’s general theory of relativity, the important quantity is energy, which includes mass (using E = mc2 – the energy contained in any object that has mass) and kinetic energy, the energy of motion. The presence of mass and energy (to paraphrase John Archibald Wheeler) dictates the behavior of spacetime; spacetime in turn affects the masses in the form of gravity. Simply having energy around causes the cosmic box to expand, just as adding air to a balloon inflates it. (It’s a metaphor of course: we aren’t adding energy from outside the universe, and of course it’s the air pressure that causes the balloon to expand.)

In a hypothetical universe dominated completely by matter, there is a delicate balancing act: too much matter means too much gravity, and the box will expand at ever more slowly over time until it stops expanding, then begins to shrink again until it collapses entirely. Too little matter means the cosmic box expands rapidly in the early times when the density was high; during later eras, gravity will slow expansion, but not enough to stop it entirely. The box expands, but the total amount of matter contained within it stays the same, so the density decreases, which slows expansion further as there is less energy to drive it. As with the cosmic box, so with the universe as a whole: expanding boxes mean an expanding universe, and shrinking boxes mean a contracting universe.

Working over several decades, astronomers determined that there isn’t nearly enough matter to make the cosmic box collapse, even accounting for the dark matter.

Light

Light obviously moves very fast: the cosmic box isn’t growing faster than light speed, so a photon can easily cross from one side of the box to the other in a finite amount of time. Light doesn’t clump up like matter does: it will travel in straight lines (assuming it doesn’t pass near something very massive) across the cosmic box. Pretending (as I suggested we can in Part 1) that the walls of the cube are perfectly reflective, a photon will bounce off the walls, exerting a tiny amount of pressure; when you add up all the photons, this pressure can be considerable. As with the ideal gas law, the pressure from light also depends on the density of photons, but that dependence for light is much stronger. The pressure persists within the “gas” of photons, even though the walls of our cosmic box are imaginary, just as we can talk about air pressure outside when there isn’t a container of air for the molecules to push against.

However, photons don’t have mass, so between that and their lack of clumping, their gravitational influence is smaller than matter. This means photons had a very large influence early in the universe when their density was large, but they don’t slow cosmic expansion much. As the cosmic box grows, their influence wanes much faster than the influence of matter. As a result of all this, though light hardly has an effect in the expansion of the universe today, it was very important in the past.

As the cosmic box expands, it will stretch light waves, making their wavelengths longer and changing their colors.

There is one additional way the growth of the cosmic box affects light, which turns out to be absolutely essential to our understanding of cosmic evolution. Imagine again that the box’s sides are reflective; as photons bounce back and forth, they form standing waves. But the box is growing, so the waves must also grow: the wavelength of the light gets larger. Since the color of light is determined by its wavelength, a photon that is (for example) initially yellow may become red as the box expands; a photon that is initially blue may become green, and so forth. Because red light has the longest wavelength in the visible spectrum, this effect is known as redshift. By measuring the redshift of distant objects such as galaxies, astronomers determine how fast the universe is expanding; this is how Vesto Slipher and Edwin Hubble discovered cosmic expansion in the 1920s.

One more note before proceeding: relativistic matter (such as neutrinos) behaves like an amalgam of non-relativistic matter and light. Since it has mass, it will have somewhat more gravitational influence than light, but it will also resist clumping. In other words, like light, it won’t have a large effect on our cosmic box in the current era, but it played a more significant role in early times.

Dark Energy and Cosmic Acceleration

Before 1998, most cosmologists were fairly certain that cosmic expansion must be decelerating, but they found acceleration instead. The difference between the possible scenarios is shown, with steady expansion added in for comparison.

Before 1998, most cosmologists were fairly certain that cosmic expansion must be slowing down. In a universe containing only matter and light, there are only two possibilities: either the density of energy is high enough to make the universe collapse back on itself, or the amount of matter is too low such that expansion continues forever, but at an ever-slowing rate as the density decreases. As the Nobel Prize-winning research suggests, however, that doesn’t seem to be the case: the expansion of the universe is accelerating, which means something other than matter and light is present inside the cosmic box.

Acceleration (left) vs. constant expansion (right): over small intervals of time, you might not notice acceleration if it's small, but over long enough stretches of time, galaxies are farther apart than they would be without dark energy. (Click to see the full-sized animation.)

That deserves repeating: light and matter as we understand them (and that includes dark matter!) in any quantity cannot make the expansion of the universe accelerate. Dark energy is the name Michael Turner coined as a placeholder for our ignorance. Nevertheless, we can say some things about dark energy beyond ruling out possibilities, and some aspects of it have a long pedigree. Albert Einstein himself proposed something like dark energy not to make acceleration, but to keep the universe static: he added an energy source known clunkily as the “cosmological constant” to general relativity to prevent the universe from expanding. He had no reason for this addition based on evidence, just a philosophical bias, and when confronted by Hubble’s evidence he removed it.

Einstein’s cosmological constant actually works as a simple version of dark energy, but there’s a problem: we don’t know how to calculate its value. If the universe were truly static as Einstein wanted, its value would be simple: it would be precisely the amount to balance out the expansion. (This is a very special value indeed: if the cosmological constant were just slightly different than the proper amount, the universe would still expand, or it would collapse back on itself, much like a pen balanced on its end will fall over at the slightest gust of air.) A calculation based on quantum field theory yields a number more than 10100 times too large (that’s a 1 with 100 zeros after it).

However, despite this problem, the cosmological constant idea is still the simplest and seems to fit the data well, even if we don’t know how to calculate it. (Alternatives include a new type of fluid not like ordinary or dark matter, a type of energy field that changes in time, and a veritable plethora of other options, most of which stretch my credibility to its breaking point. I’ll discuss one option I’m fond of in a later post.) In this scenario, whatever dark energy actually is composed of, it has a constant density no matter what size the cosmic box is. Rather than the total amount of dark energy staying the same as with matter or light, the bigger the box, the more dark energy there is inside it. Likewise, if the box shrinks, the amount of dark energy decreases.

Since we know energy drives expansion, a runaway process is the result: the bigger the box, the more dark energy there is inside it, so the box expands more. This is the same effect as a fluid having negative pressure: squeeze dark energy (don’t ask me how) and it will eagerly collapse, actively “helping” you crush it; let it grow and it won’t push back at you, and you won’t need to exert yourself.

Discussing dark energy in this way helps us understand its effects, but not much else. Without a full theory explaining where it comes from including a specific prediction for what the dark energy density is, we’re are in descriptive rather than explanatory mode. Even phrases like “vacuum energy” (which is a well-studied property of quantum field theory) are unsatisfactory unless we can calculate accurately what the density of that energy is. I admit, I do lean towards the cosmological constant/vacuum energy idea, but the burden of proof is on theoretical physicists to show why that option is superior to the others.

Coming soon: The next installment of “The Universe in a Box” will trace the history — and possible future — of the universe, and how the cosmic box helps us understand that evolution.

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10 Responses to “The Universe in a Box (Part 2): Opening the Box”


  1. 1 Tor Nelson October 28, 2011 at 23:46

    I noticed that the implication with dark energy is that energy is not conserved in the universe, in violation of a basic principle in physics that I thought still inviolable in the current theories. I found an interesting article for a general audience on that issue. Thanks for the series! http://blogs.discovermagazine.com/cosmicvariance/2010/02/22/energy-is-not-conserved/

    • 2 Matthew R. Francis October 29, 2011 at 06:21

      Yes, you noticed what I deliberately avoided mentioning: energy conservation breaks down in general relativity, and not just for dark energy. Most physicists just kind of deal with it; it bothers some (including me), but there isn’t an easy resolution and there may never be one.


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