A Dark Energy Mission

Here’s a challenge for cosmologists and aspiring science communicators out there. Most of you will know the standard cosmological model involves a thing, called Dark Energy, whose existence is inferred from observations that suggest that the expansion of the Universe appears to be accelerating.

That these observations require something a bit weird can be quickly seen by looking at the equation that governs the dynamics of the cosmic scale factor R for a simple model involving matter in the form of a perfect fluid:

\ddot{R}=-\frac{4\pi G}{3} \left( \rho + \frac{3p}{c^2}\right) R

The terms in brackets relate to the density and pressure of the fluid, respectively. If the pressure is negligible (as is the case for “dust”), then the expansion is always decelerating because the density of matter is always positive quantity; we don’t know of anything that has a negative mass.

The only way to make the expansion of such a universe actually accelerate is to fill it with some sort of stuff that has

\left( \rho + \frac{3p}{c^2} \right) < 0.

In the lingo this means that the strong energy condition must be violated; this is what the hypothetical dark energy component is introduced to do. Note that this requires the dark energy to exert negative pressure, ie it has to be, in some sense, in tension.

However, there’s something about this that seems very paradoxical. Pressure generates a force that pushes, tension corresponds to a force that pulls. In the cosmological setting, though, increasing positive pressure causes a greater deceleration while to make the universe accelerate requires tension. Why should a bigger pushing force cause the universe to slow down, while a pull causes it to speed up?

The lazy answer is to point at the equation and say “that’s what the mathematics says”, but that’s no use at all when you want to explain this to Joe Public.

Your mission, should you choose to accept it, is to explain in language appropriate to a non-expert, why a pull seems to cause a push…

Your attempts through the comments box please!


52 Responses to “A Dark Energy Mission”

  1. Grumpy Scientist Says:

    I my naive thoughts the answer’s easy. It’s like trampoline material. If it’s in tension it’s being pulled apart… Where are the springs doing the pulling? Well that’s more universe, going on forever, all pulling other bits. Not an entirely satisfactory answer il. Grant you. But better than my understanding of the physical behaviour of the inflation field.

  2. Anton Garrett Says:

    Tricky. I prided myself on qualitative explanations but the one I found hardest was, when explaining that the moon caused tides, to explain why there were TWO tides per day; the usual pub reply is “If the moon attracts the water gravitationally then you get one hump of water piled on the lunar side of the earth; why should you get another on the opposite side?”

  3. […] 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. […]

    • Greg LaBelle Says:

      I was thinking that maybe the ‘dark’ force is centrifugal. It’s happening to everything so we can’t really pick it out, we only see the result.

    • Sean,

      I would have put the “right” explanation a little differently but I definitely agree with the main points: (i) that the nature of the microscopic pressure is a complete red herring; and (ii) it’s a big mistake to think about the acceleration equation on its own, without the context of the Friedmann equation and indeed the time-slicing involved in the FLRW metric.


      PS you’ve missed a square in the Friedmann equation..

  4. The explanation is conservation of energy. Dark energy is a quantity of energy that contributes a fixed amount in a fixed volume of space. As the universe expands the amount of energy in a volume expanding with the galaxies will increase in proportion to the volume. Energy must be conserved so some other form of energy must decrease, but matter energy in an expanding volume stays almost constant while radiation energy is not enough, The only other form of energy that can compensate is the energy in the gravitational field. In the expanding volume of space the gravitational energy is negative and proportional to the square of the rate of expansion. Energy can therefore be conserved if the rate of expansion increases. That is why the dark energy is causing the expansion to accelerate.

    If you want the details with equations see my article http://vixra.org/abs/1305.0034

    • You have to be very careful with this kind of argument in GR. Energy is conserved unless you define “energy” and “conserved” very carefully..

      • Given that comment it is very clear you did not look at the article I linked.

      • telescoper Says:

        Correct. I was replying to your comment on this blog, as I am doing now..

      • Energy is given by the expression spat out by Noether’s theorem in association with time translation invariance of the combined field equations. Conservation means there is a current 4-vector whose covariant divergence is zero since this can then be integrated over a volume to give a quantity whose rate of change is euqal to the flux over the boundary. These things are now pretty standard and well known in theoretical physics and cosmology. I am not sure what other meaning someone would try to give them.

      • telescoper Says:

        My challenge was to explain what’s going on in language a lay person could understand. A lay person is far more likely to interpret energy and its conservation in a Newtonian sense, not in terms of covariant derivatives and energy-momentum tensors. As you rightly point out energy is only conserved in GR if you redefine “energy” and “conservation”. If you stick with the Newtonian concepts then energy is not conserved in GR.

      • It is because you wanted it explained in non-technical terms that I did not give the modern definitions, but the properties of energy have not changed. Energy is still a quantity that is conserved in the usual sense of what people understand by that term. It still takes a number of different forms in matter, gravity, dark energy, radiation etc, and these all add up to give the conserved total. These are principles that are familiar to anyone who has done high school science and they are sufficient to explain the way dark energy leads to accelerated expansion.

        I suggest you test the answers here by asking a non-expert if they make sense, instead of judging them in the light of your own knowledge of what technicalities might lie behind them. I think you will find that since dark energy is described as a form of energy, non-experts will appreciate an explanation based on energy conservation rather than being told that it is really some kind of tension or negative pressure or something else that it isn’t. I cant say they will prefer my short answer to a more detailed one, but I bet they choose one that talks about the properties of energy.

    • You know vixra is a crackpot website, right?

  5. John Peacock Says:


    Here’s how I try to get over this point in public talks:

    (1) First establish that the equation of motion for the universe is the same as that of a rock thrown in the earth’s gravity. Needs a detour into Newton’s result that force inside a spherical shell is zero, but this is worth knowing anyway and I’ve found people seem to accept it.

    (2) Since everyone knows that gravity slows rocks down as they rise, you can convince them that the expanding universe should slow down.

    (3) But then I say that what the rock is doing is trading kinetic energy into gravitational binding energy. Near the earth, the rock is strongly bound, and it has to give up kinetic energy if it wants to escape to infinity, where the gravitational binding tends to zero (can insert a reminder of the inverse square law here if desired).

    (4) The crux: for a sphere of vacuum, the mass isn’t constant, and rises as the cube of the radius. So rather than becoming less strongly bound as the radius increases, a particle at the periphery of such a sphere becomes *more* strongly bound, and so it must speed up as the universe expands.

    You might well complain that such energy arguments are never as physically satisfying as ones involving forces, but I’ve found this line of reasoning to be quite effective in persuading a non-expert audience (who were mostly unaware at the start of the evening that the universe is accelerating) that this is what you would expect a vacuum-dominated universe to do.

    In all of this, negative pressure is a distraction. It should only be introduced at the very end, to satisfy anyone who asks how the mass of a sphere of vacuum can increase without violating conservation of energy.

  6. See also:

    Why all these prejudices against a constant?
    Eugenio Bianchi, Carlo Rovelli

    The expansion of the observed universe appears to be accelerating. A simple explanation of this phenomenon is provided by the non-vanishing of the cosmological constant in the Einstein equations. Arguments are commonly presented to the effect that this simple explanation is not viable or not sufficient, and therefore we are facing the “great mystery” of the “nature of a dark energy”. We argue that these arguments are unconvincing, or ill-founded.


    • Thanks for the reference. I think that this is one of the most important papers in cosmology in the last 20 years or so. The authors state in the paper that there is nothing new in it, but that is precisely the point: with respect to the cosmological constant, a large fraction of the community is concerned about problems which do not exist. (If there is no problem, and someone says “there’s a problem”, and you point out “no, there is not”, then you are not saying anything new. Still, it needs to be said.)

      I made some similar arguments (supplemental to my main argument) in this paper. Alas, it has already been published, so I can’t have a “note added in proof” saying “After this work was done, the author discovered that similar arguments to those in Sect. blabla … had been made by …”. However, I gave a talk on this topic at a conference last year and fortunately, due to a change of publishers, the proceedings will appear later than planned, so I can add a note in proof there.

  7. I wrote a blogpost on the CC some years ago. You seem to be looking for an entirely verbal explanation, but I don’t believe one learns very much from that, so my piece does contain equations and probably aims past your intended audience. In any case, maybe it’s still interesting for one or the other reason


  8. Thanks,

    I am layman interested in the simplicity of the explanation so as to understand what is happening in the universe. So the challenge should one accept it….helps me.


  9. […] There has been a recent question asking people how best to explain why increasing pressure in cosmological models viewed as causing the universe to decelerate its expansion, where as an applied tension causes one to say the universe will accelerate. Some look at how that is phrased and think it sounds counterintuitive. […]

  10. I read the intent of the post to make the explanation as simple as possible, there is a lot of additional complexity I can add to this if needed, but wanted to follow what I read as intent.


  11. I answer most of my friends with reference to the spurious Newtonian derivation of the Friedmann equation. A force proportional to distance works out as a cosmological-constant term, and most people seem content with an extra force. It’s quite technical to start talking about the gravitational properties of cosmological fluids with different pressure/density ratios.

    • telescoper Says:

      Yes, it’s rather old-fashioned to think of it as being on the LHS of the Einstein equations rather than inside the energy-momentum tensor on the RHS, but it does work…

      • It’s also fun to mention that from Bertrand’s Theorem, only two force terms can produce stable, closed orbits: force inversely proportional to distance squared, and force proportional to distance.

  12. […] A Dark Energy Mission (telescoper.wordpress.com) Here’s a challenge for cosmologists and aspiring science communicators out there. Most of you will know the standard cosmological model involves a thing, called Dark Energy, whose existence is inferred from observations that suggest that the expansion of the Universe appears to be accelerating. […]

  13. A nice challenge. As far as I can see, all the answers above are either completely off-topic or entirely wrong. I attempted to give the following physical explanation to Joe Public:


    The core of the explanation is a careful computation of factors coming from the Lorentz contraction of special relativity – in a positive-pressure model of a gas.

  14. […] was spurred to ask and answer the question in the post title by Peter Coles, who specifically wanted science writers to be more clear on explaining dark energy: the name we give to the substance driving cosmic acceleration. Sean Carroll provided an […]

  15. […] Based on a Newtonian intuition of gravitation, it is often assumed in popularization that gravity is always attractive. Therefore, dark energy is often presented as the only way to explain the acceleration of the expansion of the universe which seems to push astronomical bodies apart. At the same time, it is frequently said that this dark energy has a negative pressure, even though basic intuition would suggest that a negative pressure – conversely to usual positive pressure – would tend to pull things together instead of pushing them away. Therefore, popularization readers are often left with a fuzzy statement, where one explains an apparent incoherence with an explanation that is intuitively incoherent [2]. […]

  16. Dear Peter,

    my tentative answer would be that by presenting the cosmic acceleration phenomenon as the expression of dark energy, we throw out the baby with the bath water. Instead, I believe that a good way to present the cosmic acceleration phenomenon would rather be:

    “As far as we currently know, the acceleration of the expansion of the universe is mainly due to the curvature of space-time in vacuum. Whether this curvature is due to a fundamental constant, to QFT zero energy fields or to some unknown fields that would spread everywhere, remains unknown.”

    That is at least the conclusion that I was led to in my blog post: http://truthisinthedetails.wordpress.com/2013/11/20/the-universe-is-not-filled-with-70-of-dark-energy/
    (Blog that I started after having read your post and Sean Carrol’s one on this issue :)).

    Best, Olivier.

  17. […] answering the Peter Coles’ question (which was brought to everyone’s attention by Sean […]

  18. […] a recent blog post, Peter Coles issued the challenge of explaining why the negative pressure of dark energy, that […]

  19. […] 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. […]

  20. Speaking as a non-scientist, what’s wrong with negative energy?

    Everyone knows that ice cubes emit cold, vacuum gauges measure the quantity of vacuum in your engine, and that if you reverse the leads on an LED it will emit dark instead of light. Double negatives are perfectly acceptable to Joe Public irregardless of the true sense of meaning.

    Seriously folks — it’s all metaphor. I like the trampoline thing but have two questions. What is the pressure pressing against? What are the springs pulling from? That’s perhaps the missing piece to the metaphor.

  21. […] This example comes along with the negative pressure popularization dilemma recently laid down by Peter Coles [4]. […]

  22. DARK ENERGY isn’t mysterious when you know a bit of physics. The clues are there if you know how to look.

    For example, take a look at Einstein’s stress-energy tensor on Wiki. It’s got an energy-pressure diagonal. No problem there, because we’re talking about space. Space has an innate pressure, so the universe expands like the balloon analogy you’ve seen on the Discovery Channel. But look again. That stress-energy tensor also has a shear stress term. And shear stress is the sort of thing we associate with elastic materials. And it’s there because space is something like a gin-clear ghostly elastic solid. I kid ye not. Waves run through it. Check out LIGO and they’re talking about space rippling. Imagine you flick the balloon and waves run across its skin. Get the picture?

    Now just picture that balloon for a minute. It’s actually located in a vacuum chamber to simplify the situation, and it’s actually rather similar to something called the bag model. That’s to do with the strong force and quark confinement. The harder you pull at a quark, the harder it is to pull further. OK, here’s the $64,000 dollar question: In proton-antiproton annihilation to gamma photons, where does the strong force go? And for a bonus: What keeps the photons moving at c?

    The answer is the strong force doesn’t go anywhere, because it’s the strong force that keeps the photons moving at c. Yep, because photons are waves. OK you won’t find much about this in your textbooks because there’s a bit of gap between particle physics and cosmology. There’s hints, such as on page 5 of http://arxiv.org/abs/0912.2678 where Milgrom mentions elasticity and strength. But it isn’t generally appreciated that space not only has an innate pressure, but it has an innate tension too. If it didn’t, waves wouldn’t run through it.

    Your balloon is the size it is because the internal pressure is counterbalanced by the tension in the skin. Now, how do you make that balloon bigger? You can blow some more air into it. That’s like adding more energy, increasing the pressure. But when it comes to the expanding universe, it’s a bit of a problem. Because it’s creation “ex nihilo”. It drives a coach and horses through conservation of energy, the numero uno law of physics. There’s other problems too, in that dark energy is described as negative pressure, but space has a positive energy density and a positive volume, and pressure is energy divided by volume. So the pressure can’t be negative like people say. That sucks.

    But there is another way to make that balloon bigger. Here’s a clue: bubblegum. Here’s another one: silly putty. Yes, another way to make that balloon bigger is to reduce the tensile strength of the skin. Tension is negative pressure and when you reduce the tension the balloon gets bigger until the internal pressure is reduced and balances the tension again. But as you can imagine the balloon got bigger so the skin is now thinner so the tension is reduced again, so the balloon gets bigger again. And so it goes, the universe expands, and that expansion doesn’t stop, because as space expands the “strength of space” reduces.

    The balloon is only an analogy of course. Space is more like a gin-clear ghostly elastic solid. It has no “skin”. And when you plumb the fundamentals, you find that you cannot separate space and energy. But that’s one for another day. Before that day dawns, take a look at the clear night sky. See the moon? See that star? See that gap between them? That’s space, that is. And when you know how to look, you know that you aren’t just looking at space. Because when it comes to space, there’s a lot of it about.

    And space of course, is dark.

  23. Understanding Dark Energy, at least qualitatively for the lay person, is easy if we change a fundamental notion about how the universe works. The idea of particles of matter can be shifted to the idea of matter being various structures of acoustic waves.

    These sorts of models were being studied in the late 1800’s by for instance, Bjerknes (see page 316-317 of Whittaker, “A History of the Theories of Aether and Electricity” https://archive.org/stream/historyoftheorie00whitrich#page/316/mode/2up/search/bjerknes

    Models like these are completely different from the models Michelson / Morley supposedly used to convince us that there exists no luminiferous ether because there was no ether wind blowing past the earth. The models Bjerknes and others were studying posited that what we call matter, was itself comprised of soliton (spherical standing waves) waves within, and composed of, the aether.

    The equation E=mc^2 was not known in Bjerknes time. If it were, he would have asserted that the medium of what we call empty space must be emitted during fusion reactions because the property mass, was a measure of how much of the aether ocean filling the universe had been compressed and confined within, the particular soliton wave being considered.

    In other words, a proton would have been treated as a structure of tightly coupled spherical standing waves, and electrons were considered individual spherical standing waves and so on.

    **IF** we pretend that matter is in fact comprised of some sort of wave within the ocean we call the universe (empty space) then the equation E=mc^2 tells us that Energy appears because a portion of the medium was shot out, just like we observe happen when a rocket ship takes off on the launch pad.

    When the rocket ship launches, we see large billowing clouds of gas. Those clouds of gas push the earth’s atmosphere away from the launch pad. And they also increase the volume of the earth’s atmosphere.

    The same happens when hydrogen nuclei fuse to become helium nuclei. Exothermic reactions, emit what we call space.

    It is thus no wonder that the universe is accelerating in it’s expansion. Ever since the first stars ignited, they have been flowing new space out into the unvierse we live in.

    This flow is just a slower version of the Big Bang Inflationary process. The last droplets of condensed aether (space) that were evaporating during the Big Bang, became trapped into the centers of what we today call matter.

    Fusion, exothermy, is nature’s way of continuing the vaporization process.

    Ross Tessien

    PS, Dark Mass is also a result of this same process. What we call empty space, has the property, mass. It is composed of the same stuff that matter resonances are composed. Indeed, everything within the entire universe, is comprised of nothing but aether in motion. Spacetime is a structure of acoustic standing waves. Electron, muon, tauon are individual spherical standing waves. Proton, neutron, and all of the strange particles, are composite structures of muon and tauon standing waves. And they all exist within the same aether ocean, alternately called quantum vacuum, empty space and the medium called quintessence.

    Dark Mass results due to the gradient in aether density as well as due to the slowing outward flow, and no doubt in part due to it’s having angular momentum. But Dark Mass is another story so I’ll end here.

  24. Dark energy is the binding energy of electrons in atoms – primarily hydrogen. When the atom falls into a neutron star or black hole or during a supernova this energy is returned to spacetime in the form of a volume of supposedly empty but compressed (during baryogenesis) spacetime resulting in spacetime expansion. This expansion appears to be increasing because black holes and neutron stars are growing as the nuclear matter they have been absorbing from these atoms accumulates into even bigger gravitating objects. This acceleration will eventually cease as the material falling into these objects (mostly gas) becomes exhausted. The force of gravity will then be maximized and the black holes and neutron stars will begin to merge more frequently leading to even bigger supermassive black holes. Some re-inflation will occur when bodies of matter and antimatter come into contact (even as they do now). The survivors of this epic battle will then become the black hole pairs which annihilate with enough energy for another big bang.

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