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. Coel says:

    How much is wrong with this way of explaining it?:
    The basic equations of the universe encapsulate conservation of energy.
    The density of dark energy is constant, so expansion creates more of it.
    Thus the (negative) gravitational potential energy increases.
    Thus, by conservation of energy, kinetic energy must increase.
    Hence the expansion rate increases.

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  3. Vinicius says:

    Hi, very nice post.

    I think the preassure explanation its there because of the w=-1 dispersion relation.

    I already did a cosmology course and still can ge my head around the faster than light exapansion. Espacially because my professor told me that the equations governing exapnsion could be interpreted as everything moving away from everything else, kind like if the universe started with a constant speed (in this case, acceleration).

    Could you comment on that ? How come a galaxy, in the distant future, might move away from us faster than speed of light ?

    And one more questin : If the space has a propriety which is an amount of energy, as univese expands, more energy comes in because there´s more space. So, total energy in the universe is increasing as time passes ?

    Thanks.

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  4. Jake Maier says:

    What is meant by “the universe is doubling in size?”
    Is it the distance to the end of the visible universe that is doubling, or the area, or volume?
    Volume was my first guess, but if the volume doubles per fixed time the distancing galaxies would need to decelerate or is it the radius of the visible universe that is doubling, ? What am I missing.
    Being a forester who often is satisfied with a result of 2+2~3 I readily admit that some of this is not easy to grasp for me.

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  5. Travis says:

    Sean,

    The explanation given in “The Right Way” doesn’t make sense because the normal effect of energy on the curvature of spacetime is to cause objects to get closer to each other. It seems to me that in order to explain why dark energy causes expansion, you need to explain why the effect on the curvature of spacetime due to dark energy causes the opposite of what is normally observed. The logic used in “The Right Way” would seem to imply that the mass of the sun should cause the sun to expand, albeit at an ever decreasing rate due to the energy density decreasing as the expansion occurs.

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  6. Jason Dick says:

    Very much like this explanation :) I’ve used a very similar explanation myself, but I hadn’t figured out how to do it adequately without any math at all.

    To Vinicius:
    Actually, most of the galaxies in the observable universe, by the usual definition, are currently and always have been receding from us faster than light (these galaxies are pretty far away, but there are a lot more galaxies far away than close by). The short, glib answer to this is that in General Relativity, there is no unique definition for the velocity of a far-away object. There are, instead, multiple possible definitions. Because of this, it doesn’t make sense to talk about the speed of light as being a limiting factor for the speeds of far-away objects. Instead, General Relativity only states that no object can outrun a light ray (in vacuum). A far-away galaxy with a recession velocity greater than that of light doesn’t break this rule, because it’s not outrunning any light rays traveling past it.

    That might potentially explain why it isn’t a violation of relativity for a galaxy’s recession velocity to climb faster than that of light. But it doesn’t explain why we see so many galaxies that have always had recession velocities that high.

    That answer lies in how the rate of expansion has changed over time. The expansion rate in our early universe was much, much higher than it is today, and has been decreasing steadily as matter has spread out. Early-on, when the expansion rate was very high, a photon would leave this far-away galaxy moving in our direction. But the expansion would create more space between us and that photon than the photon could travel, so that even though it was traveling towards us at the speed of light, it had still further to travel to get here. Then, later, as the expansion slowed, the photon started to make headway, eventually reaching us. The galaxy, however, only continued to get further away due to the expansion. That photon that left the galaxy long ago managed to get close enough for it to pass matter whose recession velocity became lower than the speed of light, but the far-away galaxy never did.

    Does that help?

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  7. Sean Carroll says:

    Jake– “Doubling in size” means that the distance between galaxies doubles in size. So the volume would go up by a factor of 8.

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  8. vmarko says:

    I’d say that the main source of confusion comes from the terminology — the term “dark energy” is not exactly a suitable alternative name for the cosmological constant.

    While formally one can put the CC on the other side of Einstein equations and consider it as a part of an effective stress-energy tensor, the CC doesn’t actually behave as one would intuitively expect from “energy” to behave. So trying to understand the CC as a form of energy is bound to introduce confusion and break our intuitive idea of energy as something that produces attractive gravitational forces.

    The other culprit in the confusion is that people are often told “in General Relativity the energy is the source of the gravitational field”. This is only half-true — it’s not just the energy, but also the momentum (or technically called “pressure”, “shear stress”, etc.) is a source of gravity as well. And given that in Newtonian gravity all momenta are small compared to rest masses, most people have no intuition on what momentum does to the gravitational field. With no intuition, they most often tend to simply ignore it as a source of gravity, thereby coming to wrong conclusions about the behavior of “dark energy”.

    The point is that the “dark energy” also carries along its own “dark momentum” (usually called pressure), which is three times as strong and contributes a repulsive gravitational effect. So one attractive energy plus three repulsive pressures give a net repulsive force of gravity. People who haven’t studied the details of GR have a hard time wrapping their heads around this.

    So IMHO, trying to provide an intuitive explanation for repulsive gravitational effects of dark energy is bound to fail — not because we are bad at explaining things, but because the audience (uninitiated in GR) has a hard time figuring out that energy is not the only source of gravity.

    HTH, :-)
    Marko

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  9. If the distance between galaxies double in size, does the size of each individual galaxy double in size in a corresponding manner: that is, does the distance between the stars in a galaxy double in size? If not, why is the expansion selective according to scale?

    Like or Dislike: Thumb up 4 Thumb down 0

  10. Vinicius says:

    Thanks for the answer Jason Dick.

    So you are saiyng that the velocity measurement on the galaxies gives us results faster than light but in their reference frame they are moving at lower-than-light speeds ?

    Like or Dislike: Thumb up 1 Thumb down 1

  11. Sean Carroll says:

    Philip– Galaxies (or planets, or atoms) don’t expand, because they are held together by local forces. (Gravity, in the case of galaxies.) Only freely-moving objects get pulled along with the expansion of space.

    Vinicius– What we call the “velocity” of a distant galaxy is just a fake. In GR, velocities are only well-defined when objects are moving right past each other. Distant objects, with lots of curved spacetime in between them, have an “apparent velocity” at best.

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  12. Marc Sher says:

    Sean—I agree that dropping “negative pressure” is a good idea. But there is still a source of confusion for the layperson. The first Friedman equation (typo warning – the a-dot/a term should be squared), is the same for either sign of a-dot. It gives either exponential expansion or exponential contraction for constant energy density. Most laypeople think of gravity (i.e. spacetime curvature) as always causing a contraction, and the hard part for me is explaining why more stuff makes the expansion faster….

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  13. Serge says:

    Such a simple explanation, even I can understand it (I think).

    So the term acceleration is really a misnomer when talking about expansion of the universe, since the expansion occurs at a constant rate and the “acceleration” is only apparent. I can see how that could become a pet peeve.

    Perhaps the term dark energy is also misapplied, since it is not really energy in any conventional sense. It appears to be a property of spacetime and its only interaction with matter is through its effect on spacetime. But, I guess, the same can be said about gravity — not an energy in a conventional sense and same type of interaction with matter, through its effect on spacetime (gravity warps spacetime, dark energy expands it).

    But if they are both properties of spacetime, does it make sense to try and unify them with the other forces of nature? Of course, who is to say the other forces of nature are not themselves properties of spacetime?

    Alright, I admit it, I don’t understand anything after all.

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  14. As a layperson, I will say that I find the second (right) explanation much more intelligible. But I thought dark energy was called ‘dark’ because we had no idea what it was. That we could see the effects, but not the cause or necessarily the mechanism. Has this changed?

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  15. rob says:

    Hidden due to low comment rating. Click here to see.

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  16. Sean Carroll says:

    Marc– Typo fixed, thanks. I think the confusion you point out is a good one, actually, because it helps understand what general relativity really says. It’s not just Newtonian gravity with some extra words about spacetime. It’s a dramatically different perspective, in which gravity is the curvature of spacetime. And spacetime curvature can take many different forms, depending on the distribution of energy. If you have a lump of positive energy, outside that lump spacetime will curve in such a way as to cause what looks like an attractive force. If you have a smooth distribution of constant density, the universe will expand or contract at a constant rate. What matters is that there is a balance between stuff and curvature.

    SelfAwarePatterns– Dark energy is called “dark” because it doesn’t interact with light, that’s all. In a strict sense we are not sure what it is, but there is certainly a simple and obvious candidate that fits all the data — the cosmological constant, which is what I was describing above.

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  17. Truck Captain Stumpy says:

    So… let me get this straight….
    The expansion comes in much the same way the cooling does when a firefighter uses a fog pattern of water instead of a straight stream… meaning the surface area grows exponentially with the continued growth but the actual growth is really steady (much like the water is). If that is it, then I think I can really understand it.

    Or do I have something wrong?

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  18. sagredo says:

    If there is no pressure, then what is the first law of thermodynamics for de Sitter space?

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  19. Sagredo says:

    In the case of the accelerating expansion
    dU=єdV, where є is the energy density, є=const.
    But work would have to be done to cause the region to expand,
    dW=-pdV. Then p=-є.
    It is the negative pressure which is the driving force behind the accelerating expansion. Should we ban the negative pressure?

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  20. AI says:

    Ok, but since the concept of scale is relative could the expansion of the Universe be reinterpreted as contraction of everything in it? Here the amount of space would stay the same but the dimensions of everything else – galaxies, stars, us – would shrink with time. Would Einstein equations still apply to this case? Could the energy momentum tensor be somehow modified for them to apply? Or are there some fundamental reasons why this picture is ruled out?

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  21. 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.

    http://arxiv.org/abs/1002.3966

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  22. Bee says:

    You need either both equations, or you need one and stress-energy conservation. Either way you turn it, the pressure will come in. You’ve implicitly used stress-energy conservation by starting on the assumption that you’re dealing with a source that is constant over time.

    That having been said, I like your explanation. The explanation that I myself hate most is saying that dark energy acts like ‘antigravitation’. Because I once made the effort of trying to take this idea seriously and now I’m like the only person on the planet who knows that antigravitation does not act like dark energy. (If you think about it, it’s trivial. Whatever antigravitating matter you have, it’s still matter. It’ll never give you the right w value, regardless of whether its energy density is positive or negative.)

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  23. James Cross says:

    “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.”

    I thought observations have shown about 4 billion years the expansion began to speed up. Can it the rate be constant and fixed if it is changing?

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  24. platohagel says:

    I am a layman, so how would it be better explained to me that you might help me understand this challenge?

    R for a simple model involving matter in the form of a perfect fluid:

    and then to have,

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

    This is a interesting view to me, and at the same time I am asking what do you have in terms of the naturalness of what exists in the universe to explain this?

    I am drawn to spherical cows in terms of explanations and to this, being only an approximate, I wonder what evidence exists as to contribute to that expansion? So you take “a region in space” and examine it? The collapse of a supernova, knowing it had a pre-existent state, what is geometrically happening through that evolution?

    I am following of course with interest.

    Best,

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  25. Andy Odell says:

    Sorry, but I think there is a fundamental mistake in this. Hubble’s constant is constant in space (we would measure the same value no matter which galaxy we live in), but not necessarily in time. In fact, the inverse of H (called the Hubble time, the time it would take each galaxy to get to its current distance at current velocity), is sometimes called the age of the universe; this implies that if H were constant, then the age of the universe presumably wouldn’t change with time? A varying H implies that the energy density also varies with time; not a problem, energy is conserved, but not energy density.

    Most beginning astronomy students make this same mistake (though much more naively) – that ‘velocity proportional to distance’ applies to a given object – as its distance increases, so does its velocity. But this is incorrect.

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  26. Matt says:

    Sean–

    I’ve run into this same problem when teaching GR to my own students. But after I tried a simple explanation of the sort you describe here, one of my more inquisitive students asked me why the story changes if we were to imagine flipping the sign of the cosmological constant. I didn’t know what to say except point back to the Friedmann equations (and the Raychaudhuri equation)!

    So I put this challenge to you — if the explanation is as straightforward as you describe it in “The Right Way,” then how does one intuitively explain why the universe goes from accelerated expansion to accelerated contraction if we change the sign of the cosmological constant, going from a dS-like solution to an AdS-like solution?

    Thanks!

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  27. George says:

    Am I missing something, as it seems this means that on the whole the total energy of the universe is increasing? If the universe expands and the dark energy density stays constant throughout, then there is more total energy moment to moment?

    Like or Dislike: Thumb up 1 Thumb down 0

  28. vmarko says:

    @ George:

    “Am I missing something, as it seems this means that on the whole the total energy of the universe is increasing?”

    Yes, you missed to read this:

    http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

    HTH, :-)
    Marko

    Like or Dislike: Thumb up 2 Thumb down 0

  29. George says:

    Thanks Marko, that certainly helps. I think it will take a bit to internalize this!

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  30. Sean Carroll says:

    Bee– I didn’t use the pressure, I used the dependence of the density on the scale factor. You can derive that dependence from the equation of state, but you could equally well derive the equation of state from the scale-factor dependence. Neither is more fundamental.

    James– The expansion *rate* (the Hubble parameter) has always been decreasing. But recently its rate of decrease has become so small that the velocity of galaxies is increasing.

    Andy– I was speaking in an approximation where there is only constant dark energy, in which case the Hubble constant actually is constant.

    Matt– It’s more complicated when Lambda < 0, because there are no solutions with zero curvature and no other forms of energy density. But the basic physics is still the same. Ordinary matter dilutes away, eventually the vacuum energy dominates, the universe decelerates, then matter begins to dominate once again and you crunch.

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  32. Michael Carasik says:

    I very much appreciate “the right way,” as I had just read a “negative pressure” explanation on Friday which made no sense to me.

    What I continue not to understand is this: If space itself is expanding, why don’t our measurement units expand similarly so that the expansion is transparent to us?

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  33. What about (hypothesized) particles as explanation: the ‘fat’ graviton, ‘chameleon’, …

    Fat Gravity Particle Gives Clues to Dark Energy
    Force-carrying “gravitons” with mass could help to explain the universe’s accelerating expansion
    scientificamerican.com/article.cfm?id=fat-gravity-particle-gives-clues-to-dark-energy

    Dark-energy particle spotted?
    Reported ‘chameleon’ particle would change its mass to match its environs.
    nature.com/news/2009/090529/full/news.2009.531.html

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  34. kashyap vasavada says:

    How about this argument based on elementary thermodynamics. dq = du + pdv = 0 for an isolated system. If energy density of vacuum is constant positive , u has to increase with increasing volume. Vacuum cannot be diluted! So du > 0. Then for dv > 0, p has to be negative. For the case when Lambda is negative (Matt’s question) this will also work because in that case du 0. Anyone sees problem with this argument?

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  35. kashyap vasavada says:

    How about this argument based on elementary thermodynamics. dq = du + pdv = 0 for an isolated system. If energy density of vacuum is constant positive (Lambda > 0) , u has to increase with increasing volume. Vacuum cannot be diluted! There is more vacuum. So du > 0. Then for dv > 0, p has to be negative. For the case when Lambda is negative (Matt’s question) this will also work because in that case du 0 Anyone sees problem with this argument?
    I had some problem in editing. Please ignore the previous comment.

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  36. kashyap vasavada says:

    Sorry to take so much space. Again problem with the editor. In the 6th line in the above I should have du < 0.

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  37. Confused says:

    Jason Dick “That answer lies in how the rate of expansion has changed over time. The expansion rate in our early universe was much, much higher than it is today, and has been decreasing steadily as matter has spread out. Early-on, when the expansion rate was very high, a photon would leave this far-away galaxy moving in our direction.”

    Sean Carroll “James– The expansion *rate* (the Hubble parameter) has always been decreasing. But recently its rate of decrease has become so small that the velocity of galaxies is increasing.”

    “… a long time ago, the Universe was actually expanding more slowly than it is today.” http://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy/

    And you wonder why the lay person is confused! I can recall physicists explaining with absolute certainty that our moon formed from a ring of debris around the Earth that coalesced by gravitational attraction to form our satellite. But wait! No, an asteroid hit the Earth and a large chunk of our planet broke away. No, wait, our satellite was formed when… And all of this is pronounced with such conviction!
    After many years spent in abandoned mines almost a mile deep, there has been no trace, whatsoever, of anything that can be attributed to dark matter yet this is a forgone conclusion.

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  39. Hal Swyers says:

    I kept this even more simplistic, but thought that was the intent of the original challenge

    http://thefurloff.com/2013/11/17/the-universe-and-pressure/

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  40. Victor says:

    How about this explanation:

    Suppose that you live in a small apartment in which your many belongings make it look really messy. If you move to a larger place, say a mansion, with the same belongings, your house should logically look less messy. But mysteriously this very expectation is violated in our universe; a fact which has baffled very smart physicists for so long. Measurements prove that we are constantly, here exponentially, moving to a larger world as time passes. Yet the calculations of space-time dynamic based on Friedmann equations show that to keep this rate of expansion, our new mansion should look as messy, here better to say as massy, as before. Put it other way, there should be some phantom belongings in our apartment, alternatively phantom galaxies in our universe, often called dark matter by cosmologists, not yet seen and measured, that stay with us no matter what and fill up this continuously, exponentially, expanding space-time.

    What more puzzles me is what could be or occur on the boundary of our universe spacetime, what is beyond the farthest away galaxies? If this huge bubble is expanding so what is there outside of it?!

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  41. Bee says:

    Sean: How do you know the ‘dependence of density on the scale factor’ without knowing the equation of state for which you need the pressure? You’ve basically postulated it (as I said, you assumed it’s constant), but we both know you’re not allowed to do this in GR. You can pick an initial value, the rest is dictated by the theory. And for that you need the pressure. You’ve just avoided that by picking a time-dependence that you like and avoid telling us that it’ll only solve the equations of motion if you have a negative pressure.

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  42. “So the term acceleration is really a misnomer when talking about expansion of the universe, since the expansion occurs at a constant rate and the “acceleration” is only apparent. “

    No, it is not a misnomer. By “constant” Sean means that (in the limit where the cosmological constant is the only important thing) the expansion is exponential.

    Like or Dislike: Thumb up 1 Thumb down 0

  43. From the point of view of the Friedmann equations, introducing a positive cosmological term is equivalent to adding some negative pressure, as we can see
    in this Wikipedia page about FLRW. In FLRW, just by looking at the geometry of the universe, there is no way to tell whether a cosmological term is present, or when there is more negative pressure. I think this is why people say that expansion is caused by negative pressure, and I see nothing wrong with this.

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  44. “Sorry, but I think there is a fundamental mistake in this.”

    No, Sean is correct.

    “Hubble’s constant is constant in space (we would measure the same value no matter which galaxy we live in), but not necessarily in time. In fact, the inverse of H (called the Hubble time, the time it would take each galaxy to get to its current distance at current velocity), is sometimes called the age of the universe; this implies that if H were constant, then the age of the universe presumably wouldn’t change with time?”

    Right. I admit that there is some confusion, since the “constant” in the Hubble constant means it is only a constant in space at a given time (the actual origin is that is a constant in an equation like m and b constants in y = mx + b) while the cosmological constant is constant in time.

    “A varying H implies that the energy density also varies with time; not a problem, energy is conserved, but not energy density.”

    Energy is not conserved in GR or cosmology, at least not in the sense in which this is normally understood.

    Without the cosmological constant, in general H is not constant in time. So, this fact does not imply the cosmological constant.

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  45. N. says:

    Great post, thank you Sean.

    How does all this look in the eyes of MOND?

    Or is that horse dead already?

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  46. supermuf says:

    The tricky part is explaining why “expanding at a fixed rate” means “accelerating.”

    The point is that the new expanded space also expands, that’s the reason for the exponential rate.

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  47. meh says:

    I think vmarko hit the nail on the head. Most people do not ever learn the intricacies of General Relativity. Though I squirm as I type that because it’s not like the fundamental concept of dark energy is too complicated to teach to a high school physics class. That being said, I think every high school student should take calculus by their senior year; and that certainly doesn’t happen.

    I understand, and prefer, the negative pressure explanation because it helps me visualize what is happening and implies the deformation of space. In my experience, the people that have difficulty understanding dark energy usually don’t want to understand it. Tends to be the same people that think scientists are involved in a conspiracy that involves tricking governments into paying for their Bugatti Veyron, mansions, and stripper laden pool parties…you know, crazies…who must be silenced if our plans are to succeed.

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  48. kashyap vasavada says:

    @vmarko: I am aware of the fact that many people believe energy is not conserved in GR. But don’t you use energy conservation in thermodyamaics to get the second equation. If there are alternate derivations directly from GR (without using thermodynamics) doesn’t it lead to some conflict somewhere?

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  49. meh says:

    N.,

    MOND :: Newton’s gravity

    TeVeS :: Einstein’s gravity

    I think those are both generally restricted to dark matter.

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  50. Pingback: Why Does Dark Energy Make the Universe Accelerate? | Daniel W Ostler's Travel Blog ©

  51. Gizelle Janine says:

    @vmarko: Oh that conservation stuff is a b$&@? when you get into non-zero…baby. :D

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  52. vmarko says:

    @ kashyap vasavada:

    “I am aware of the fact that many people believe energy is not conserved in GR.”

    This is not a matter of belief. Conservation laws are tightly connected to global symmetries via the theorem of Emmy Noether. In particular, the conservation of energy is a consequence of the global symmetry of time translations. If this symmetry exists in a given physical system, energy is conserved. If it doesn’t exist, energy is not conserved. When the physical system is the entire universe (i.e. when studying cosmology), one can check that time translations are not a symmetry. Consequently, the energy is not conserved.

    “If there are alternate derivations directly from GR (without using thermodynamics) doesn’t it lead to some conflict somewhere?”

    Shortly put — there are, and it doesn’t. Basically, you specify (at initial moment) the matter content and all their nongravitational interactions, plug all that into Einstein equations, and from there you can derive a detailed evolution of both matter and geometry. Including the laws of thermodynamics. The whole thing is self-consistent, and in the appropriate special cases it reduces to what we already know (ordinary thermodynamics, Newtonian mechanics, classical electrodynamics, etc.), courtesy of the equivalence principle.

    But you need to be aware that the “ordinary” thermodynamics (as you know it from non-GR physics courses) is only a special case of the “real thing”, which can be derived from Einstein equations. When you look at your tabletop experiment, the ordinary version and GR-version of the first law of thermodynamics are practically indistingushable, due to the fact that CC effects are extremely small for tabletop volumes of gases etc. But when you increase the volume of your gas to cosmological scales, the CC correction to the first law of thermodynamics becomes important, and then you can see that energy is not really conserved.

    Also, there are no inconsistencies in the whole story. Most notably, the CC correction to the first law of thermodynamics still does not allow you to make a perpetuum-mobile or some such stuff… ;-)

    HTH, :-)
    Marko

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  53. Serge says:

    Seems to me, if you say “constant expansion rate” means doubling in size over a constant time interval, then the acceleration is automatically built in. In fact, the only thing constant here is the acceleration itself.

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  54. Hasse says:

    Than you Sean.
    I’ve been reading a lot of articles about this, and just been more and more confused over the different explanations. I have been trying to understand this by building different mathematical models – most dynamic simulations, and your article gives me a lot of confidence that I’m on the right way.

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  55. N. says:

    As I can see, nobody wants to discuss MOND. All I wanted to know, was, is the idea stlill alive or buried?

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  56. vmarko says:

    Sean’s article and dark energy have nothing to do with dark matter and MOND. Discussing MOND would only confuse the readers even more.

    HTH, :-)
    Marko

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  57. Jake Maier says:

    Marko,
    Isn’t a perpetuum mobile possible with superconductive material?
    Jake

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  58. DEL says:

    By saying that dark energy is persistent, constant throughout space and time and a feature of space itself, do you mean to say it’s of the infamous ‘cosmological constant’ variety? If so, why is this an explanation? It seems more like a just-so fudge factor constrained to preserve some feature of the equations ol’ Einstein deemed essential. And if it’s a property of space itself, one wonders how it gets its specific value and why isn’t that value derivable from other universal constants, such as the speed of light, the gravitational constant, Planck’s constant, etc.

    So, the amount of stuff in the universe is fixed, hence spacetime has a fixed curvature, hence the universe has a fixed expansion rate, hence galaxies are seen to accelerate away from each other. Clear and simple, isn’t it? So how come it was such a big shocking surprise, back in 1997, when the acceleration discovery was first reported?

    Also, if I recall right, the history of the cosmological expansion is quite complex, going from deceleration into acceleration about 5*10^9 years ago. Is this consistent with the constancy of the cosmological constant? Are there theories in which dark energy is a substance rather than a feature of space itself, and by which space can do all kinds of outrageous tricks?

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  59. Lino says:

    Sean:

    How is it that dark energy “persists”? In an expanding universe, how does it remain ‘constant’?

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  60. George says:

    So I have a thought experiment that might help me understand this more thoroughly. Or maybe criticism of my formulating the thought experiment itself will help me.

    If I have a fixed vessel filled only with space, choose any scale for this vessel. This space will expand, but it is constrained. So does it expand in any sense? If no, then placing a shell around the current universe would stop inflation?

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  61. N. says:

    ->Marko
    Right. I am a reader and I am confused :))

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  62. N. says:

    Now then, why is everybody so certain that space-time is a consecutive continuum? We know there are singularities, why not discontinuites? We all know the distribution of the strong force, would it really be something extravagant to suppose that gravity (space-time if you wish) behaves similarly?

    I’m just trying to think out of the box; call it my crackopt theory of the week :)

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  63. Jake Maier says:

    I thought discontinuities exist in singularities as wormholes.
    At least hypothetically.

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  64. Nemo says:

    “The tricky part is explaining why “expanding at a fixed rate” means “accelerating.” ”

    Try this: “Suppose you have a colony of rabbits with a fixed, constant birth rate per capita. What happens to the population?”

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  66. Jim Cross says:

    Sean,

    After you see the responses here, how successful do you think you have been?

    “Dark energy is persistent, which imparts a constant impulse to the expansion of the universe, which makes galaxies accelerate away.”

    I think I got that but I think I already understood that.

    “But recently its rate of decrease has become so small that the velocity of galaxies is increasing.”

    Maybe my expectation was for an explanation for that but maybe that isn’t understood yet.

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  67. “Also, if I recall right, the history of the cosmological expansion is quite complex, going from deceleration into acceleration about 5*10^9 years ago. Is this consistent with the constancy of the cosmological constant? “

    I wouldn’t call that “quite complex”. Yes, it is consistent. Any introductory cosmology book which discusses the cosmological constant should cover this.

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  68. Space/time is not constant; space x time is constant. The expansion of the universe is accelerating. The reason why is invisible. That is because one does not see why.

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  69. Gizelle Janine says:

    I don’t know what happen to my previous comment…but the jist was “I have no clue why non-zero has nothing to do with expansion of the universe” and then a worried face. No explanation?

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  70. DEL says:

    To Phillip Helbig:
    You caught me–I’m neither a professional cosmologist nor an aspiring cosmology student, so I’ve missed that “Any introductory cosmology book.” (My introductory cosmology belongs to the era before the accelerated expansion was discovered.) Yet I infer from the discussion that, theoretically, matter-energy dominated the dynamics in the beginning, causing deceleration, which turned into acceleration once dark energy took over.
    But if that’s correct, and if matter-energy is conserved, and if dark energy behaves as simply as an absolute constant, and if the universe composition is as found by WMAP, then it should be relatively straightforward to construct the history of the scale factor and compare it with whatever results from up-to-date supernovae observations. Was that done? If so, how good is the agreement?
    Nothing would please me more than to learn the the agreement is so-so, because I think the cosmological constant is a wart on Einstein’s equations, though dark energy as a substance is even worse. (As an uncommitted amateur, who does not make a living or reputation out of papers admitted, I can afford such a stance and crave scientific revolutions.)

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  71. Gizelle Janine says:

    Edit: My bad… F$&@!

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  72. Anthony Aguirre says:

    Hi Sean,

    Preparing for a recent lecture, I realized you can derive the repulsive action of positive vacuum energy in pretty much the same way you can derive the Friedmann Equations from Newton’s gravity, if you treat a spherical uniform ball and ignore the exterior. If you ascribe a potential energy V[r]=-Mm/r to the a particle of mass m near the ball of mass M, and let M=M_stuff+M_vac, there M_vac is the vacuum energy density times the volume of the ball, then when you take -dV/dr for a force, you find the usual Newtonian term, then a term that goes as R and is repulsive. In words: the gravitational potential energy of normal stuff becomes less negative when you expand the ball, but the contribution from vacuum energy becomes more negative. Forces act so as to lower potential energy, so this leads to an attractive force due to the stuff, but a repulsive one due to the vacuum energy.

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  74. Thomas Walsh says:

    What if in, your first Friedmann equation, G is not a constant at all. G is an ‘accepted value’. Why is this acceptable? My understanding is that over many years and many experiments, the measure of G varies by almost +/- 1.5%. It’s not that measurements are getting closer to the ‘real’ value; but, the measurements flutter around the +/- 1.5%. Wish you could do an study/article on the many experimental measurements of G (or what amounted to a measurement), Cavendish to today…

    If G is not a constant at all, then perhaps gravity is not only a geometry but is also a physical process. After all, electro-magnetism existed as a physical process long before it was either discovered or used. In short, does ‘dark energy’ really exist or is it just an artifact of theory?

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  75. cayle says:

    The number of beings that can compute in parallel (and compactify time) tends to increase do to intelligence being a neotonizing force (via domestication).

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  76. Nemo says:

    Anthony Aguirre said: “Preparing for a recent lecture, I realized you can derive the repulsive action of positive vacuum energy in pretty much the same way you can derive the Friedmann Equations from Newton’s gravity, if you treat a spherical uniform ball and ignore the exterior.”

    Yes, I teach that too. BUT I stress to the students that “ignoring the exterior” means that you are NOT dealing with a homogeneous, isotropic universe like ours. When I teach this stuff I emphasise that what we are really doing is proving that FRW *cannot* be deduced at all from Newtonian gravity. In more technical language: no [3-]vector theory of gravity can give a sensible cosmological model, because a non-trivial 3-vector cannot be isotropic.

    In fact, the nice thing about cosmology is that it immediately makes it clear that all talk of “gravitational force” must be wrong — forces cannot be isotropic. This is why SC’s campaign to rid us of pressure is such a good idea: we have to teach people to get away from the whole concept of “gravitational force”.

    SC’s idea of stressing the constancy of the dark energy density is an excellent one. He just needs to find an intuitive way of explaining geodesic deviation, as applied to the geodesic worldlines of galaxies in an isotropic homogeneous universe.

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  77. “SC’s idea of stressing the constancy of the dark energy density …..”.

    According to me the constancy of the energy in the universe is quod erat expectandum.

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  78. …energy density…

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  79. kashyap vasavada says:

    @vmarko: Thanks for the reply to my question. I see your main point. However, I am not sure if the difference between relativistic and non-relativistic thermodynamics is just due to CC (I am not sure if you are saying that.). Creation of additional space (expansion) does require additional energy which has to come from somewhere. Also the universe will keep on expanding for a while even without CC, although eventually it has to collapse because of normal gravity. It seems that such problems have been ignored in cosmology.

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  80. “Yet I infer from the discussion that, theoretically, matter-energy dominated the dynamics in the beginning, causing deceleration, which turned into acceleration once dark energy took over.”

    .
    Exactly. Since the energy density of the cosmological constant is, errm, constant, while that of matter is inversely proportional to volume (radiation is more complicated, but taking it into account introduces only small corrections), at early times the universe is matter-dominated and at late times, if the cosmological constant is positive, approaches exponential expansion. So, a relatively complicated outcome, if you like, from a simple premise—like most of the universe.

    .
    “But if that’s correct, and if matter-energy is conserved, and if dark energy behaves as simply as an absolute constant, and if the universe composition is as found by WMAP, then it should be relatively straightforward to construct the history of the scale factor and compare it with whatever results from up-to-date supernovae observations. Was that done? If so, how good is the agreement?”

    .
    Well, a Nobel Prize was awarded for it not long ago. The theory behind the Nobel Prize is literally textbook stuff, but that is not what it was awarded for. It was awarded for the enormous observational effort and the attention to detail to make sure that what are believed to be standard candles (or can be corrected to behave as such) really are. (This is common in astronomy. To measure the Hubble constant, in theory all you need is one distance and the corresponding redshift. The devil is in the details.) Yes, it does fit—remarkably well. In fact, for the first time we have a standard cosmological model which fits essentially all the data. (Caveat for experts: Initial analysis of PLANCK results confirms some discrepancies at low l but, considering how good the fit is at high l, I suspect that the solution here will be instrumental and/or involve the CMB and keep the “cosmological standard model” intact.

    .
    “Nothing would please me more than to learn the the agreement is so-so, because I think the cosmological constant is a wart on Einstein’s equations, though dark energy as a substance is even worse.”

    .
    No, it is quite good. It is very good. It looks like a pure cosmological constant (w=-1). While one should be open to the possibility that it is not a pure cosmological constant, at the moment there is not one shred of evidence for this and a pure cosmological constant fits all observations (with the same value of the cosmological constant, of course). In other words, “dark energy” (as Sean pointed out a while back, this is a terrible name; it’s a shame his “smooth tension” didn’t catch on) is the cosmological constant. A rose, by any other name…but I prefer to call it the cosmological constant, or lambda.

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  81. kashyap vasavada says:

    @ Sean: I think these controversies again bring up the point that it is hopeless to try to understand theoretical physics without equations. Remember your write up “most embarrassing graph in physics” ? All these efforts are turning futile because we are trying to put these complex non classical phenomena in human languages which are based on our everyday life which is classical!!!

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  83. DEL says:

    Phillip Helbig: Thank you, I’m beginning to really enjoy this conversation.

    I have been following the observational effort–the subject of the recent Nobel prize–more closely than the theoretical background and am therefore more acquainted with it, qualitatively, though.

    About the agreement between the CC-comprising model and the best, up-to-date, observational results (“…it is quite good. It is very good.”) what I would like not to miss is seeing the actual comparison and getting elated over it myself. I’d appreciate if you post the relevant (free-access) link/s. Thank you again.

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  84. vmarko says:

    @ DEL:

    “About the agreement between the CC-comprising model and the best, up-to-date, observational results (“…it is quite good. It is very good.”) what I would like not to miss is seeing the actual comparison”

    You can start here:

    http://en.wikipedia.org/wiki/Lambda-CDM_model

    Most importantly, look at the table of parameters and their values. The error-bars can give you a feeling of how well the experimental data fits the theory.

    HTH, :-)
    Marko

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  86. DEL says:

    Thanks, Marko.
    Most of the things in the lambda-CDM Wikipedia article were known to me. What I miss, and maybe you can refer me to, is, e.g., this: a plot of the world lines of participating type-Ia supernovae progenitors according to the lambda-CDM model (pretending they all lie on a single ray and have existed since ever,) compared with the observed world events of their explosions.

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  87. Pingback: Why Does the Space-Time’s Curvature in Vacuum Make the Universe Accelerate? | The truth is in the details

  88. Ricky says:

    Here’s an interesting post about the explanation for dark energy:

    http://m0tls.blogspot.com/2013/11/its-harmful-to-teach-wrong-physics.html

    Oops. Change the first 0 to o in the above URL.

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  89. Fireworks says:

    One way to understand why Sean’s claims are wrong is the following:

    — The goal is to explain to the layperson the following; why can gravity be sometimes repulsive rather than attractive, in the sense that galaxies will on average accelerate away from each other rather than towards each other. We can begin by imaging a homogeneous universe that is static at some moment in time, then we let it go….will it attract or repel?

    According to Sean, the answer is always to turn to the (first) Friedmann equation. Well we definitely need to include curvature, and we have:

    H^2 = rho – k/a^2

    where k is the curvature. Initially, let us imagine that things are at rest, so H=0, then rho-k/a^2=0 (which can be used to solve for k). The question is then: what happens next, does it collapse (which in this context is the same as attract or decelerate) or does it expand (which in this context is the same as repel or accelerate)?

    An answer to this requires knowing about the SECOND TIME DERIVATE of the scale factor. And the first Friedman equation above is really hopeless at telling us what this is. Instead we need an equation for a”; which comes from the second Friedman equation and includes pressure.

    Then to discover if it will accelerate or decelerate we absolutely need to know about the value of the pressure.

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  91. phayes says:

    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.

    It seems to me it’s only wrong because a pressure is being confused with (the effect of) a difference between two +ive pressures at a boundary there. From the POV of a test particle inside the balloon the pressure due to the gas is felt as an isotropic crushing. Negate that and the wrongness goes away, surely?

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  92. Gary Godfrey says:

    Included with an explanation of why DE makes the universe accelerate should be a summary of why it is exciting. The phenomenon of Dark Energy is one of those rare discoveries that illuminate the inadequacy of a present theory (GR). As Sean emphasized, the extra DE curvature is extraordinary because it appears to be constant in time. So either:
    1) DE is just a new dimensional (1/length^2) constant Lambda whose explanation lies beyond GR and also seems to be beyond quantum field theory, or
    2) Move Lambda to the right hand side of Einstein’s field equation and interpret it as an energy density. Unfortunately, a density should decrease as the universe expands, but DE is constant. Furthermore, the DE density is negative while all matter (that we know) has positive energy density.

    Both alternatives lead to the conclusion that GR (and our understanding that only an energy density causes curvature) just doesn’t have the ability to explain the DE phenomenon (beyond just calling it Einstein’s cosmological constant). DE is a big clue to something new! We need a new reason both for a constant curvature, and for the curvature to have a sign opposite to that caused by normal matter !

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  93. d says:

    tidal forces can compress or stretch, and (divergence of) the *deviation acceleration* of galaxies does pick up the pressure term…

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  94. “Included with an explanation of why DE makes the universe accelerate should be a summary of why it is exciting. The phenomenon of Dark Energy is one of those rare discoveries that illuminate the inadequacy of a present theory (GR). “
    .
    Huh? There is no evidence that dark energy is anything other than the cosmological constant, and this was introduced by Einstein. So how does it somehow illuminate the inadequacy of the present theory?
    .
    OK, we don’t know what, if anything, it is, whatever that means. But isn’t it enough to know that it exists and is described by the theory? IIRC it was Wheeler who summarized GR as “spacetime tells matter how to move; matter tells spacetime how to curve”. However, we don’t know why this is the case.

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  95. Masses are continuously absorbing or emitting energy. On balance the quantity of energy emitted is enormous but not taken account of in the calculations based on the Standard Cosmological Model and the mainstream understanding of gravity..

    The consequence of what I have said in my comment on “Is time real?” is that gravity is related to mass and not to energy and momentum like pseudo-gravity.

    Therefore, according to me, the question of what causes the acceleration of the expansion of the universe has nothing to do with DM/DE, pressing or stretching, whether you like it or dislike it.

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  96. Yair says:

    Dear Prof Carrol,

    In a laymen’s attempt to distinguish “apparent” velocity and “regular” velocity, whereby:
    * “Apparent” velocity – the velocity you artificially associate to a distant galaxy relative say to earth.
    * “Regular” velocity – velocity in the sense that fits, say, into a special relativity energy calculation

    In my simplistic mind, “pushing” a galaxy till it obtains a regular velocity v – requires energy E that is a function of v.

    The special relativity expression for energy explodes when you reach the speed of light.

    Does this imply that: (several – not necessarily distinct – options that come to my confused mind):
    * You cannot plug “Apparent” velocity into these energy calculations
    * There is no relationship between the energy content in space-time and the kinetic energy i am trying to think about.
    * Other…

    With regards to option 2,
    Using your “The Right Way” explanation, trying to think about “pushing” a galaxy until it recedes from us in more than speed of light,
    I can imagine that any amount of energy in spacetime will do.

    The only thing that would change – is how long will we have to wait.
    With a small amount of energy, we will just have to wait longer.

    If that is the case – than it is to me – a clear cut demonstration of the difference between apparent and regular velocities.

    It is very impressive and rewarding to see a top tier Scientist dedicating precious time to public outreach.
    I hope you will find enough of a general interest in my question to merit an answer.

    Yair

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  97. vmarko says:

    Yair,

    Imagine a rubber sheet which is being stretched away indefinitely, and put two marbles on it. One marble (our galaxy) can in principle move with respect to the rubber directly beneath it. Its velocity with respect to this rubber cannot exceed the speed of light, and is the “regular” velocity. The other marble (distant galaxy) is further away on the rubber sheet, and it may move with respect to rubber directly beneath it, with velocity again only less than speed of light. That is also the “regular” velocity.

    However, at any point in time, you can measure the distance between the two marbles/galaxies, along the straightest possible line on the rubber sheet. Now, even if the “regular” velocities of the two marbles are always kept zero, the distance between them will grow, since the rubber in between is being stretched. If you divide this distance with time, you get the “apparent” velocity. This velocity has nothing to do with the motion of matter through space (but only with the motion of the space itself), so there is no speed-of-light limit.

    As for energy balance, you need to invest some energy to move each marble with respect to the piece of rubber it’s standing on, and it takes an ever-growing amount of energy to make the marble’s “regular” velocity closer to the speed of light. On the other hand, there is absolutely nothing needed to invest in order to make the “apparent” velocity as large as you like, because that velocity is the property of the motion of space itself, rather than matter through space.

    In order to get this stretching motion of “space itself” appropriately consistent with observations, we need to plug a nonzero (positive) cosmological constant term into Einstein equations of general relativity. It is commonly called “dark energy”, but I still claim that this is a very unfortunate terminology. It is more than just “energy”, and it behaves in a way in which any ordinary energy would never behave.

    Finally, note that in general relativity energy is not conserved — at least not in a way you would expect — regardless of the presence or absence of any CC, dark energy, etc. Therefore you should not even try to think about the kinetic energy balance between galaxies, because there is no balance and there is not supposed to be any.

    HTH, :-)
    Marko

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  98. Thomas Rizzo says:

    Dr Carroll,
    If Dark Matter is keeping the Milky Way Galaxy together, why do we often hear that the acceleration of the Universe will effect us? I understand that the Universe is accelerating, but doesn’t Dark Matter keep the Galaxy together therfore not having an effect on “us”?

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  99. Mark Foskey says:

    Is there a reason it’s described as energy rather than mass? Could you just as well give it in kg/m^3? Or does mass/energy equivalence break down here somehow?

    It’s not obvious to me that constant curvature implies a constant proportional rate of expansion. I don’t think I have a good enough intuitive notion of what 4D curvature looks like to make inferences like that about it. Is there a way to explain how you measure curvature in spacetime that makes the relationship between curvature and constant expansion clear?

    Does it work to imagine rockets (actually unpowered probes) heading in opposite directions, and then having one sending a beam of light back to the other? That gives you a triangle and you can look at the angle sum and compare it to pi. If there’s an angle deficit then that suggests the probes are accelerating apart. So if my way of measuring curvature is right, then I guess I do buy the claim that constant curvature across spacetime leads to a constant “growth rate of space”. But my reasoning might be completely wrong.

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  100. Stuart says:

    @Sean

    Congratulations for your award winning book.A great read indeed!
    For those of you who like me are constantly seeking to answer the questions ;what is Dark Matter?and What is Dark Energy? you can find my views to these questions in a paper I wrote http://dx.doi.org/10.4236/ijaa.2013.33028. Please excuse me for the missing 2pi in the expression r=2pi/k

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  101. 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!

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  102. @ Philip Helbig

    OK, OK, 1 Like for you.

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  103. 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.

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  104. @ 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.

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  105. 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

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  106. 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

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  107. “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.

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  108. 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

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  109. 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.

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  110. 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.

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  111. 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
    http://www.circlon.com/home/7-Photon-Energy.html

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  112. Apparently Not says:

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

    http://www.nature.com/news/cosmologist-claims-universe-may-not-be-expanding-1.13379

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  113. 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.

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  114. 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.

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  115. 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.

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  116. 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.

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

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  118. 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).

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  119. david klien says:

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

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  120. 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?

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