Why Does Dark Energy Make the Universe Accelerate?

Peter Coles has issued a challenge: explain why dark energy makes the universe accelerate in terms that are understandable to non-scientists. This is a pet peeve of mine — any number of fellow cosmologists will recall me haranguing them about it over coffee at conferences — but I’m not sure I’ve ever blogged about it directly, so here goes. In three parts: the wrong way, the right way, and the math.

The Wrong Way

Ordinary matter acts to slow down the expansion of the universe. That makes intuitive sense, because the matter is exerting a gravitational force, acting to pull things together. So why does dark energy seem to push things apart?

The usual (wrong) way to explain this is to point out that dark energy has “negative pressure.” The kind of pressure we are most familiar with, in a balloon or an inflated tire, pushing out on the membrane enclosing it. But negative pressure — tension — is more like a stretched string or rubber band, pulling in rather than pushing out. And dark energy has negative pressure, so that makes the universe accelerate.

If the kindly cosmologist is both lazy and fortunate, that little bit of word salad will suffice. But it makes no sense at all, as Peter points out. Why do we go through all the conceptual effort of explaining that negative pressure corresponds to a pull, and then quickly mumble that this accounts for why galaxies are pushed apart?

So the slightly more careful cosmologist has to explain that the direct action of this negative pressure is completely impotent, because it’s equal in all directions and cancels out. (That’s a bit of a lie as well, of course; it’s really because you don’t interact directly with the dark energy, so you don’t feel pressure of any sort, but admitting that runs the risk of making it all seem even more confusing.) What matters, according to this line of fast talk, is the gravitational effect of the negative pressure. And in Einstein’s general relativity, unlike Newtonian gravity, both the pressure and the energy contribute to the force of gravity. The negative pressure associated with dark energy is so large that it overcomes the positive (attractive) impulse of the energy itself, so the net effect is a push rather than a pull.

This explanation isn’t wrong; it does track the actual equations. But it’s not the slightest bit of help in bringing people to any real understanding. It simply replaces one question (why does dark energy cause acceleration?) with two facts that need to be taken on faith (dark energy has negative pressure, and gravity is sourced by a sum of energy and pressure). The listener goes away with, at best, the impression that something profound has just happened rather than any actual understanding.

The Right Way

The right way is to not mention pressure at all, positive or negative. For cosmological dynamics, the relevant fact about dark energy isn’t its pressure, it’s that it’s persistent. It doesn’t dilute away as the universe expands. And this is even a fact that can be explained, by saying that dark energy isn’t a collection of particles growing less dense as space expands, but instead is (according to our simplest and best models) a feature of space itself. The amount of dark energy is constant throughout both space and time: about one hundred-millionth of an erg per cubic centimeter. It doesn’t dilute away, even as space expands.

Given that, all you need to accept is that Einstein’s formulation of gravity says “the curvature of spacetime is proportional to the amount of stuff within it.” (The technical version of “curvature of spacetime” is the Einstein tensor, and the technical version of “stuff” is the energy-momentum tensor.) In the case of an expanding universe, the manifestation of spacetime curvature is simply the fact that space is expanding. (There can also be spatial curvature, but that seems negligible in the real world, so why complicate things.)

So: the density of dark energy is constant, which means the curvature of spacetime is constant, which means that the universe expands at a fixed rate.

The tricky part is explaining why “expanding at a fixed rate” means “accelerating.” But this is a subtlety worth clarifying, as it helps distinguish between the expansion of the universe and the speed of a physical object like a moving car, and perhaps will help someone down the road not get confused about the universe “expanding faster than light.” (A confusion which many trained cosmologists who really should know better continue to fall into.)

The point is that the expansion rate of the universe is not a speed. It’s a timescale — the time it takes the universe to double in size (or expand by one percent, or whatever, depending on your conventions). It couldn’t possibly be a speed, because the apparent velocity of distant galaxies is not a constant number, it’s proportional to their distance. When we say “the expansion rate of the universe is a constant,” we mean it takes a fixed amount of time for the universe to double in size. So if we look at any one particular galaxy, in roughly ten billion years it will be twice as far away; in twenty billion years (twice that time) it will be four times as far away; in thirty billion years it will be eight times that far away, and so on. It’s accelerating away from us, exponentially. “Constant expansion rate” implies “accelerated motion away from us” for individual objects.

There’s absolutely no reason why a non-scientist shouldn’t be able to follow why dark energy makes the universe accelerate, given just a bit of willingness to think about it. Dark energy is persistent, which imparts a constant impulse to the expansion of the universe, which makes galaxies accelerate away. No negative pressures, no double-talk.

The Math

So why are people tempted to talk about negative pressure? As Peter says, there is an equation for the second derivative (roughly, the acceleration) of the universe, which looks like this:

\frac{\ddot a}{a} = -\frac{4\pi G}{3}(\rho + 3p) .

(I use a for the scale factor rather than R, and sensibly set c=1.) Here, ρ is the energy density and p is the pressure. To get acceleration, you want the second derivative to be positive, and there’s a minus sign outside the right-hand side, so we want (ρ + 3p) to be negative. The data say the dark energy density is positive, so a negative pressure is just the trick.

But, while that’s a perfectly good equation — the “second Friedmann equation” — it’s not the one anyone actually uses to solve for the evolution of the universe. It’s much nicer to use the first Friedmann equation, which involves the first derivative of the scale factor rather than its second derivative (spatial curvature set to zero for convenience):

H^2 \equiv \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho.

Here H is the Hubble parameter, which is what we mean when we say “the expansion rate.” You notice a couple of nice things about this equation. First, the pressure doesn’t appear. The expansion rate is simply driven by the energy density ρ. It’s completely consistent with the first equation, as they are related to each other by an equation that encodes energy-momentum conservation, and the pressure does make an appearance there. Second, a constant energy density straightforwardly implies a constant expansion rate H. So no problem at all: a persistent source of energy causes the universe to accelerate.

Banning “negative pressure” from popular expositions of cosmology would be a great step forward. It’s a legitimate scientific concept, but is more often employed to give the illusion of understanding rather than any actual insight.

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120 Responses to Why Does Dark Energy Make the Universe Accelerate?

  1. Although I just read them today, some of the sentiments in my last comment above were echoed a few years ago here: http://arxiv.org/abs/1002.3966

    So, if you don’t believe me, believe Carlo Rovelli!

  2. @ Philip Helbig

    OK, OK, 1 Like for you.

  3. Mark Foskey says:

    Forgot the metric isn’t Euclidean. I think that invalidates my triangles approach. But that’s the kind of explanation I’d love to see.

  4. @ Mark Foskey

    Triangle approach: I do not know if you mean the same but Renate Loll of the University of Nijmegen in the Netherlands is working on a triangle approach on sub-atomic scale of how space-time funtions.

  5. Agron says:

    First I want to understand, which are the facts that universe is expanding. Could somebody please write down to the blog those facts. I am so confused with universe expansion. It looks to me instead the space-time is expanding with the speed of light. Can we start a discussion on that topic.

    Thanks for your consideration

  6. Stuart says:

    In my research I have found that dark energy is a low energy graviton of energy =hH where h is the planck constant and H the Hubble constant being emitted by spacetime. From which we find lambda=3(H/c)^2

  7. “First I want to understand, which are the facts that universe is expanding. Could somebody please write down to the blog those facts. I am so confused with universe expansion. It looks to me instead the space-time is expanding with the speed of light. Can we start a discussion on that topic.”

    A blog is not the right place for this. Read Cosmology: The Science of the Universe by Edward R. Harrison. It is by far the best introductory cosmology textbook. It is accessible to non-experts without oversimplifying things. Please, please, please read this book if you are seriously interested in understanding cosmology. Please.

  8. Agron says:

    Thank you Phillip Helbig that’s a good suggestion.
    Let me put my opinion below:
    1. First the known world was explained by gods, that lasted for thousands of years.
    2. Then explained by geocentric system which lasted if am not wrong for circa 1500 years.
    3. Then heliocentric system which lives for say for 400 years and still make sense.
    4. Then known world was expanded in galaxies and today is explained by universe which opinion lives for say 100 years , while there are many debates about.
    Does everybody see a trend in time , so thousand years, 1500 years, 100 years ….
    But the debate in this blog is about the expansion of universe, which for everybody is a given by the only one fact “redshift” or “Doppler effect”.
    Let’s come to “Doppler effect” phenomenon.
    It states that if a source of sound goes towards an observer the frequency is increased, while the wave length decreased. When the source of sound passes the observer then frequency is decreased while the wave length increased. That’s true and that way “redshift” is explained by analogy.
    But there is another explanation:
    If the source of sound doesn’t move, but is stationary in some place, while the observer moves from some distant towards that source and measures both the frequency and the wave length of the sound.
    I am quite sure that he would measure increased frequency and decreased wave length, then when he reaches the sound source and he starts to move away, I am enough sure his measurement would be in opposite , so decreased frequency and increased wave length.
    What does that tells you. That tells you that redshift could be explained without implying that universe is expanding.
    Sorry everybody by this simple explanation, but what I have read so far says that universe is expanding because of the “redshift” captured on the light spectrum emitted by all known galaxies in universe. But that “redshift” couldn’t be explained only in one way. Galaxies maybe are stationary but nature of spectrum of light itself is that it becomes “red” i.e. “redshift” when it reaches the observer.

    Welcomed comments

  9. DEL says:

    Agron: The lifespan of theories is getting shorter, simply because scientific research is intensifying exponentially and the technology and instrumentation available to it advance as fast as smartphone technology…

    As to Doppler’s, if it were true that the Earth is moving while the galaxies are stationary, galaxies in the direction of the Earth’s motion would have redshifted spectra, those in the opposite direction would have blue-shifted spectra and those perpendicular to the motion would have their spectra unchanged. But this is not the case: ALL (far enough) galaxies are seen redshifted, in proportion to their distance from us. And since we shouldn’t assume we have a special status in the universe (think Copernicus,) then we must assume that this picture is true for all galaxies—they all recede from each other. So, unless you come up with a really ingenious and valid alternative explanation, this can only mean that the whole universe of gallaxies is expanding. Luckily, Einstein’s theory of general relativity predicts this expansion, and even its acceleration, though not quantitatively.

  10. Agron says:

    I did not say that Earth is moving and galaxies are stationary. All of them are moving but not expanding! All the information we humans get comes from the spectrum of light, even in everyday life here on Earth. But the spectrum of the light generated from the source initially has high energy which means (depending on energy) is “blueshift” then traveling towards the observer tends always to becoming “redshift” , because it is losing energy. Red light has always less energy than blue light. That’s why we see “redshift”. Sorry guys this is my last comment.

  11. Apparently Not says:

    DEL says:
    …then we must assume that this picture is true for all galaxies—they all recede from each other.

    Actually, the Andomeda and Milky Way galaxies are on a collision course. Moreover, apparently this is not the first time in that they nearly collided 10 billion years ago.

    We know next to nothing about photons. If light has mass, as it apparently does, sharpen your pencils. More than one cosmologist has come to the conclusion that the universe IS NOT EXPANDING! I concur and said so on my website in 2003. If there is more than one viable explanation for red shift, then all bets are off.

    See “Photon Energy, Mass, Velocity And Wavelength – The Living Universe” at

  12. Apparently Not says:

    Please SEE ALSO: Cosmologist claims Universe may not be expanding : Nature News & Comment


  13. DEL says:

    Apparently Not:

    Apparently, that’s not what I meant. Three lines above what you cite I wrote “ALL (far enough)…” I believed it would be tedious to repeat this reservation next to every “all” and that readers have longer memory than what it takes to proceed three lines.

    I also wrote “unless you come up with a really ingenious and valid alternative explanation…” So, here you are, provided massive photons turn out valid.

  14. DEL says:

    Apparently Not: Alright, I’ve read it. But if the idea leads to an infinitely old universe (which appears at first glance to be implied by a stationary universe that lacks an initial singularity) then old problems thought to be dead and buried resurrect: (1) Olbers’ paradox, (2) the universe not being thermodynamically dead yet, (3) and maybe more…

    I love heresy but, personally, I don’t believe this one has a chance.

  15. Guilty says:

    Guilty as charged. But here’s my concern:

    Young unfettered, creative minds are immersed in “conventional wisdom” from day one. If you expect to find employment upon graduation, one must regurgitate the gospel because your peers have a vested interest in the “Big Bang”, i.e., book sales, professorships, tenure, etc. Try obtaining funding in the form of a grant if you don’t “conform.” And how many seminars do you think you’ll attend – damn few. It’s essentially reinforced “group think” and we are ALL guilty of it – politics and organized religion come to mind.

    As the website states, and I quote, “Others say that Wetterich’s interpretation could help to keep cosmologists from becoming entrenched in one way of thinking. “The field of cosmology these days is converging on a standard model, centred around inflation and the Big Bang,” says physicist Arjun Berera at the University of Edinburgh, UK. ‘This is why it’s as important as ever, before we get too comfortable, to see if there are alternative explanations consistent with all known observation.'”

    Yes, it is “heresy” and that’s the problem! It shouldn’t be. Keep an open mind. Hey, the Flat Earth Society still holds regular meetings. And ask yourself how long it took for “conventional wisdom” to accept the fact that the Earth was not at the center of the universe.

    Truly understanding the photon, it’s behavior and it’s properties, is IMHO the alpha and the omega and we’ve just (in the last hundred years) started knocking at the door. DM and DE may just be amusing “bar banter” in a few short (exponential knowledge growth) years.

  16. DEL says:

    Guilty: That’s how science works. It’s not perfect, it’s not ideal, it’s not above human, but a better method has yet to be invented. Like democracy, it’s a terrible system but the alternatives are even worse. And it’s probably irreparable, because its faults are basically of social-anthropological origin.

    Read your Kuhn. Science advances as paradigms shift by scientific revolutions. Paradigms first entrench themselves, then defend themselves ferociously, then collapse to give way to newer paradigms. In between revolutions, in the era of “normal science,” all the evils you plead guilty to characterize the scene. But in the long run they are probably necessary and productive evils: just think of a system in which all revolutionary and heretical ideas are treated politically correct, getting equal attention, funding and journal space.

    And things aren’t all that bleak: after all, Wetterich’s idea did get a voice in Nature, didn’t it, and it wasn’t scoffed at either.

  17. Why Does Dark Energy Make the Universe Accelerate?
    Because we are being sucked into it.

  18. David says:

    I believe the universe is accelerating outward because of intense gravity from a thick uniform outer shell of dark matter (quantum fog) at the leading edge of the universe originating from the big bang. Sincerely, Dave. Age 7. (Just kidding, but obviously, I’m no scientist).

  19. david klien says:

    I thought I understood Dark energy till I read this blog. Now I am confused !

  20. dichotomy says:

    Expand or contract a volume by an equal amount, and the new shell like radius of the equal amount follows an equation; original radius* {[(1+x)^(1/n)] – [(x)^(1/n)]},m. where n is the number of dimensions , assume only 3 and you have both holes and shells, fractional and even amounts for x, truncate the curve at x=zero, shell radius =1, at x= -1/2 the volumes fully contract to a disc of radius = original radius*(~1.5874), go beyond – 1/2 to -1 and you get expanding holes. Why the volumes contract or expand by equal amounts needs further thought! Why would a disc go on to expand into a hole and a volume from the same moment, to form a virtual particle pair?