Date: December 21, 2011
Title: What is Dark Energy?
Podcaster: Rob Knop
Organization: Question University Canada
Links: My home page : http://www.sonic.net/~rknop
MICA : http://www.mica-vw.org
MICA Public Events : http://www.questu.ca
Description: We know from observations of distant supernovae that the expansion of the Universe is accelerating. How can this be? Gravity would normally pull things together and cause an expansion to slow down! Dark Energy is the name we give to this mysterious substance that drives the expansion. In this podcast, I’ll discuss what little we do know about Dark Energy, and how we think about it as we try to learn more.
Bio: Rob Knop obtained a PhD in Physics from Caltech in 1997. He then worked with the Supernova Cosmology Project and was part of the discovery that the expansion of the Universe is accelerating. After six years as an assistant professor at Vanderbilt University, he worked in the computer industry for two years. He now teaches physics the new college Quest Unviersity in British Columbia. He gives regular astronomy talks in Second Life in association with the Meta-Institute of Computational Astronomy.
Sponsor: This episode of “365 Days of Astronomy” is brought to you by Distant Suns astronomy app for iPad and iPhone is proud to sponsor this episode of 365 Days of Astronomy. Multiple award winning Distant Suns has been your guide to the cosmos for over 25 years. Distant Suns has all the features you need to make stargazing fun and easy. It’s also a great gift – for any occasion – holidays, birthdays… or anytime. And iTunes makes it simple to give Distant Suns as a gift. Get Distant Suns astronomy app on iTunes today.
Transcript:
WHAT IS DARK ENERGY?
Hello, and thank you for listening to 365 Days of Astronomy! I am Rob Knop, professor of physical science at Quest University Canada.
I’ve talked about the discovery of the accelerating Universe in a couple of recent podcasts here, the discovery that won this year’s Nobel Prize in Physics. You might wonder why I can’t just shut up about this Nobel Prize, and the truth is, I just think it’s really cool. Not only that the Nobel Prize went to astronomy work, and cosmology work in particular, but also that it was research that I was a major part of when the discovery was made.
So the Universe is accelerating. In the October 25 podcast for 365 Days of Astronomy, I talked about what it meant to say that the Universe is expanding, and that that expansion is accelerating. Today, I want to talk about what little we know about why the Universe is accelerating. First, why is that surprising? Well, the Universe is filled with stuff. Normally, with gravity, we think about stuff being pulled towards each other. If the Universe is expanding, stuff is moving apart; the action of gravity, then, would be to slow down that expansion, as the force of gravity tried to pull everything back together. But, when we went and measured the expansion history of the Universe, we found that in fact the expansion is speeding up. To explain this, we say that the Universe is filled with a mysterious substance called “Dark Energy”, a substance that has a negative gravitational effect. That is, its gravity pushes things apart rather than pulls things together.
So what, exactly, is Dark Energy? The truth is we don’t know. It’s the name we give to our ignorance. This is not to say that we don’t have ideas about it. Indeed, one idea is that Dark Energy isn’t stuff at all, but is rather a pointer that our theories of gravity are breaking down on the largest scales. In this way, it might be analogous to the Luminiferous Aether of the turn of the 20th century, the hypothesized medium which light moved relative to. In fact, the Luminiferous Aether wasn’t real stuff at all; that it was postulated was a pointer that our theories had broken down, and were no longer adequately explaining reality to the level to which we were able to measure it. It was ultimately replaced by the theory of Special Relativity, the theory that extended the Newtonian theories of mechanics that work at speeds much less than the speed of light. It’s possible that Dark Energy is the same sort of thing, an indication that our theory of gravity, General Relativity, isn’t working quite right on Universal scales.
For the rest of this podcast, however, I am going to assume that General Relativity– an extremely well-tested theory that we know predicts the right things on a wide range of spatial scales– is right, and still applies even to the Universe as a whole. If that is the case, then we need for there to be some stuff, some Dark Energy, in order to explain the observed acceleration of the Universe’s expansion.
We can say a bit more than that, however. It’s not just, “well, the Universe is expanding, so, uh, how about we say, um, there’s Dark Energy, yeah, that’s it, that’s what’s happening!” In order to cause the Universe to expand as described by General Relativity, Dark Energy has to have some particular properties. In order to understand what those are, however, we need to talk about gravity.
In a traditional, Newtonian view, mass causes gravity. The Earth orbits the Sun because the great mass of the Sun exerts a gravitational force on the Earth, holding it in orbit. You could say, in Newton’s theory, that mass is the source of gravity. However, our modern theory of gravity– which does give the same answers as Newton’s theory for things like satellites orbiting the Earth or the Earth orbiting the Sun– is called General Relativity. In order to understand the source of gravity in General Relativity, we have to go back to one of the core equations of relativity, and indeed one of the most famous equations: E=mc^2.
What does E=mc^2 mean? On the left, E stands for energy. On the right, m stands for mass, and c stands for the speed of light. What this equation is saying is that mass is just a form of energy; the equation is the conversion factor that allows you to figure out how much energy, in energy units like Joules or calories or kilowatt-hours, there is in a certain amount of mass (mass coming in mass units like grams or kilograms). Mass and energy are, in a sense, the same thing. Well, that’s not quite right, because there are forms of energy other than mass, but mass is just one form of energy. Now, because the speed of light is a “big number”, in everyday life mc^2 is going to be much, much larger than any other form of energy we deal with. For example, if a car is going 100~km/h, the amount of energy in its motion– its kinetic energy– is one hundred thousand billion times smaller than mc^2, the amount of energy in the mass of the car.
In General Relativity, it is not mass that is the source of gravity, but rather energy. Indeed, whereas in Newton’s gravity we often deal with a lot of individual masses and add up the effects of all of those masses to figure out the gravitational force, in General Relativity we have to consider the energy density at a point in space, and in all nearby points of space, to figure out what gravity is going to be like anywhere. Remembering that as long as things aren’t moving near the speed of light, the vast majority of the total energy of something is its mass energy, that means that much of the time, the difference between the energy density, and the energy density just from mass, is insignificant. So, it’s fair to say that most of the time, the source of gravity in General Relativity is indeed just mass density, just like in traditional gravity.
However, it doesn’t have to be that way. It turns out that in the very early Universe (before it was 100 thousand years old or so), the energy density in radiation, in light, was higher than the energy density in matter. As you probably know, the photon, the particle of light, has zero mass. This means that in the early Universe, gravity was dominated by the density of stuff that had zero mass… but it did not have zero energy. (What happened to all of the energy density in that light? It was redshifted away. As the Universe expands, so do the wavelengths of photons. Each photon loses energy, to the point that today, the energy density in photons is insignificant compared to the energy density in normal matter.)
In order to describe the source of gravity in General Relativity, then, we can’t just talk about mass, but we have to talk about energy in general. For the simplest sorts of fluids– a fluid being just some stuff that can be in space– we can parametrize its energy density in two ways. First, there is just its energy density, how much energy is there. Second, there is its pressure.
Wait, how does pressure come into this? You may know what pressure is from talking about air pressure. Think about trying to squeeze an inflated rubber balloon, for example. On a microscopic level, where does this pressure come from? It comes from the motions of the molecules. When you try to squeeze the balloon, it resists. The reason it resists is that all of the air molecules inside the balloon are bouncing off of the walls of the balloon, trying to push it back out. So, pressure is related to the motions of molecules. And, because there is energy– kinetic energy– in motion, pressure represents the energy density as a result of that motion.
It’s important to remember this. We’re not talking about pressure as something that is exerting a force itself. Yes, it does; air pressure supports a balloon, and water pressure can crush you if you go too deep under water. But, for gravity, that’s not important. What’s important is that pressure is a stand-in for the amount of energy there is in the motion of the molecules, or the particles, of a fluid.
Let’s think about normal matter. Normal matter, in the form of galaxies, is typically moving around at speeds much less than the speed of light. For that reason, its pressure is insignificant compared to its energy density, where its energy is mostly in its mass by E=mc^2. You may be surprised to find out that cosmologists would describe air as having “zero pressure”. What they really mean by that is that the energy density in the motion of air molecules, represented by its pressure, is a whole heck of a lot less than the mass energy density of air. So, normal matter has zero pressure.
In General Relativity, as applied to the expansion of the Universe, the source of gravity is the energy density, plus three times the pressure. Again, remember that pressure here isn’t pushing anything around, the way you usually think of pressure, but rather pressure is standing in as a way of representing that part of the energy density that has to do with the motions of particles. For normal matter, the pressure is effectively zero, as I already described. For radiation– that is, things like light, that is, photons– the pressure is one third of the energy density. For radiation, the source of gravity is higher for a given amount of energy density than it is just for mass, as I said before.
So, let’s think about this. If the source of gravity is the energy density plus three times the pressure, then if you have a negative pressure, and it’s negative enough, then you’ll have something that gives you a negative source of gravity. This is how Dark Energy is defined. It’s something whose pressure is equal to less than negative one third its energy density.
What does negative pressure mean? It’s more like a tension. If you try to squeeze a rubber balloon, the pressure pushes back out on you. If you try to stretch a rubber band, its tensions tries to pull it back on itself. “But wait!” you may be saying now. “I thought negative pressure made the Universe expand faster!” It does. Again, don’t fall into the trap of thinking that it’s the pressure itself driving this expansion. Rather, it’s the gravity that results from this pressure. That we’re talking about pressure at all is perhaps a little misleading; we’re talking about how the dynamics of the material relates to the energy density of the material. And, thinking about it in those terms, I have to admit that I have a hard time imaging just what “negative pressure” really means.
So what can have negative pressure? The most obvious example is vacuum energy. Start with a region of space. Take out everything from that region of space; take out all the atoms, all the photons, all the neutrinos, all the dark matter, so that there’s nothing left. When there’s nothing left, as a result of quantum mechanics, there may still be some residual energy density. This energy density is the energy of the vacuum; the energy that’s present just in space itself. This vacuum energy density has negative pressure; indeed, it turns out that the pressure of vacuum energy is equal to negative one times the energy density. If you put that into the equation for the source of gravity, which is related to the energy density plus three times the pressure, you get a source of gravity equal to negative two times the vacuum energy density. So, vacuum energy is one possibility for Dark Energy; indeed, many people think it’s the most likely possibility.
You may have heard of Einstein’s cosmological constant. This was a term that Einstein realized he could introduce into his equations of General Relativity without modifying the theory. He introduced it because when he applied the theory to the Universe as a whole, he found out it had to be either expanding or contracting. At the time, everybody believed that the Universe was static. Einstein introduced the cosmological constant, which had a negative gravitational effect, in order to balance the attraction of all the mass and achieve a tenuous balance that led to an unstable, but static Universe. Shortly thereafter, when we discovered that the Universe is indeed expanding, Einstein tossed out the cosmological constant, and called introducing it to make his theory predict a static Universe his biggest blunder. After all, if he hadn’t done that, he could have predicted the expansion of the Universe before it was observed, and he could have been famous.
The cosmological constant, it turns out, is directly related to the density of vacuum energy. Indeed, the terms cosmological constant and vacuum energy density are effectively interchangeable. So, you could say that the cosmological constant is one possibility for Dark Energy; it’s just that it’s exactly the same possibility as is vacuum energy.
There are lots of other possibilities for Dark Energy; all of these have a pressure that is negative, but not exactly equal to the negative of the energy density of whatever stuff it is. As we try to set limits on just what Dark Energy might be, we do experiments that are sensitive to the ratio between the pressure and energy density of Dark Energy. This will affect the expansion history of the Universe, as well as some other things. We use the letter w for this ratio; w is the pressure of Dark Energy divided by the energy density of Dark Energy. If w=-1, then Dark Energy is just vacuum energy.
Right now, the best limits on w tell us that it’s probably around -1, with an uncertainty less than ±0.1. It would be big news if we could figure out that w is different from -1, even just a little bit, for that would mean that Dark Energy can’t be vacuum energy. So far, however, as we’ve been shrinking the error bars on w, they’ve stayed consistent with -1. We can never prove that it’s exactly -1, we can only improve those error bars. As long as the situation stays as it is right now, we will be able to say that our measurements are consistent with Dark Energy being vacuum energy, but we won’t be able to rule out everything else.
There are other reasons to believe that vacuum energy is real. One is quantum field theory. It predicts that there ought to be some left over energy at the “zero point”, or vacuum level, of all the various quantum fields that exist. For each particle– photon, electron, neutrino, whatever– there is a corresponding quantum field. The result of these vacuum quantum fields have been measured in the Casimir Effect. Two metal plates put right next to each other in a vacuum experience a force between each other as a result of some specific wavelengths of the quantum fields being excluded by the small distance between the two plates.
There is a problem with our theoretical understanding of these quantum fields, however. A naive calculation from quantum field theory of how high the vacuum energy density should be gives a number that is 120 orders of magnitude larger than what we measure from the expansion of the Universe! If the vacuum energy were truly that large, the Universe would have expanded exponentially early on, far too fast for galaxies ever to have had time to form. This factor of ten to the 120th is often considered to be one of the worst theoretical predictions in all of physics. So, we’re left with thinking that vacuum energy might be real from quantum field theory, but with the unsatisfying situation of its measured value being vastly different from what our current theory predicts.
Is Dark Energy vacuum energy? Maybe. Probably. But it might be something else. It’s safe to say in any event that we do not completely understand Dark Energy, and indeed our understanding is weak enough that Dark Energy may not be stuff at all, but may be a pointer to the break down of our theories on Universe-size scales. However, Dark Energy may well be stuff, and it may be vacuum energy, or it may be something even more exotic. Cosmologists are trying to learn more about Dark Energy by measuring w, this ratio of its pressure to its energy density; that’s the first parameter after its raw density that we can even attempt to measure. Hopefully, in the next decade or two, we’ll learn something about w, and maybe also about how much w has changed, if at all, through the history of the Universe.
Thank you for listening to 365 Days of Astronomy!
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365 Days of Astronomy
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