The surprising discovery that the universe is not just expanding but that the *rate* of expansion is increasing is what led to the idea of dark energy as the cause of that acceleration. But explaining in non-mathematical terms to a lay audience why dark energy leads to an accelerating expansion is not easy and introducing the idea that dark energy creates a negative pressure does not help much either.

Sean Carroll, one of the best expositors of cosmology to non-scientists, tries to explain what is going on.

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.

…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.”

…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.

It is still not easy to understand but definitely one of the better attempts that I have seen.

## 34 comments

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## wtfwhateverd00d

November 17, 2013 at 2:22 pm (UTC -4) Link to this comment

Is it energy as in Thermodynamics? The characteristic of never being diluted as space expands seems to suggest energy is being created or transformed. Where does dark energy come from that it does not dilute? Does it obey the First Law of Thermodynamics?

## sundoga

November 17, 2013 at 2:22 pm (UTC -4) Link to this comment

That makes a lot more sense than anything I’d heard before. By slowing down and

explaining his terms, Carroll avoids one of the biggest traps in reprting science – using words the publicthinkthey understand, but actually don’t in this context.It shows something I’ve long believed – science CAN be explained to the layman without dumbing it down, as long as you remember your audience and their underlying knowledge base.

## jaxkayaker

November 17, 2013 at 2:41 pm (UTC -4) Link to this comment

If I remember my basic physics correctly, when velocity is constant, acceleration is zero. When velocity is changing, acceleration is nonzero. Acceleration itself may be constant or not, either of which will result in changing velocity. If the foregoing is correct, is sound like Carroll is saying that the acceleration of the expansion of the universe is constant.

It seems that part of the confusion is that normally velocity is a change in distance per unit time, with the distance measured in only one spatial dimension. However, the expansion of the universe takes place in three spatial dimensions.

## Rob Grigjanis

November 17, 2013 at 2:53 pm (UTC -4) Link to this comment

That phrasing makes it sound like we have the slightest idea what dark energy is. My understanding is that dark energy is a fudge factor we came up with to account for accelerated expansion. For example, just adjusting the cosmological constant in Einstein’s field equation so that it describes what we observe. Maybe it should be called kludge energy.

## Pierce R. Butler

November 17, 2013 at 3:30 pm (UTC -4) Link to this comment

I (dimly) grasp the concept of acceleration as a consequence of the inverse-square law: as space expands, the gravitational attraction of everything from grains of dust to galactic megaclusters to each other weakens, and so separation increases a little bit more with each Planck interval than it did the last.

Does this make any (approximate) sense?

## Rob Grigjanis

November 17, 2013 at 3:33 pm (UTC -4) Link to this comment

In this case, the first law says dU = -PdV (change in energy=minus pressure times change in volume).

Because the dark energy density is constant, contracting a region of DE actually decreases the energy, so the pressure is negative. This means that an expanding region of space is doing negative work, which balances the increase.

## mnb0

November 17, 2013 at 3:40 pm (UTC -4) Link to this comment

While I teach physics I never studied it at a university. Still the concept of dark energy is clear to me. Two points.

1. I worry about testability, besides the simple fact that the Universe expands as it expands.

2. “it takes a fixed amount of time for the universe to double in size”

If we divide the two we get a quantity we can sub the acceleration of the Universe, also called the increase of speed. Of course if this is a feature of space it only applies to the University as a whole and we can’t apply it to far away stars or something. Still it seems to me it’s more than just “a timescale”.

Am I missing something?

## raven

November 17, 2013 at 3:46 pm (UTC -4) Link to this comment

So Dark Energy is an intrinsic property of space. Whatever that means. This implies that “space” whatever that is, is being continuously created. And space does have an energy level, the vacuum level is greater than zero. So energy is being continuously created.

Or I don’t quite get it, always possible with modern Cosmology.

It always amazes me that we know little about what most of the universe is made of, Dark Energy and Dark Matter.

## raven

November 17, 2013 at 3:51 pm (UTC -4) Link to this comment

If Sean Carroll is correct, there won’t be a Big Rip someday. That is at least good to know. For shorter distances, the rate of expansion is too slow and will never be enough to tear everything apart.

The farther away galaxies will just keep accelerating until they go beyond the event horizon and disappear.

FWIW, a static universe is unstable. Gravity would just condense everything some day. You have to have a Big Bang and/or Dark Energy to keep that from happening.

And Intelligent Design, my foot. Someday the universe will end up cold and dark and dead for our kind of life.

## wtfwhateverd00d

November 17, 2013 at 4:06 pm (UTC -4) Link to this comment

Thanks, that helps a bit — makes me think of the universe as a spring.

## Matt G

November 17, 2013 at 4:25 pm (UTC -4) Link to this comment

Mano, what do you think about the idea that the expansion of the Universe is due to our 3D Universe residing on the surface of a 4D “sphere” which is expanding? Can’t remember where I read this, but it was not more than a couple of months ago.

## lpetrich

November 17, 2013 at 4:27 pm (UTC -4) Link to this comment

Actually, one can get the behavior of dark energy by inserting its equation of state into the pressure-work equation:

P = – U/V

The minus sign here is a feature, not a bug: negative pressure

d(- P*V) + P*dV = – dP*V

So dP = 0 — constant pressure, and thus constant mass/energy density

## Mano Singham

November 17, 2013 at 4:34 pm (UTC -4) Link to this comment

Yes, that is correct but what we are talking about is the rate of increase of this separation. This depends on the energy density of the universe. Normally this density would decrease as the universe expands and hence the rate of increase would get smaller with time. But with a constant dark energy density, the rate of increase also remains constant.

## Mano Singham

November 17, 2013 at 4:44 pm (UTC -4) Link to this comment

What we are talking about is an expansion in the fabric of space. Galaxies are embedded in this fabric and are largely carried along with it, except for some small local motion.

## Mano Singham

November 17, 2013 at 4:46 pm (UTC -4) Link to this comment

This idea of a 4D sphere is sometimes used to explain the curvature of space. I don’t think it adds anything of value for this question.

## michaelbusch

November 17, 2013 at 4:47 pm (UTC -4) Link to this comment

Note also that dark energy follows the

secondlaw of thermodynamics: entropy increases as the number of available energy states in a system increases, and increasing the size of the space and dropping the energy of the photons in it is a very good way to increase the number of available states and so the entropy.## michaelbusch

November 17, 2013 at 4:48 pm (UTC -4) Link to this comment

I once heard a suggestion that we should call it “levity”, in contrast to gravity. This was not taken seriously.

## michaelbusch

November 17, 2013 at 5:01 pm (UTC -4) Link to this comment

Not quite right. The model Carroll has described is exponential expansion. If that continues without end, after a sufficient number of doubling times the expansion rate will be so high that everything that isn’t a black hole will be ripped apart – but by that point, everything that is currently in the local group of galaxies we are in would have cascaded down to black holes and assorted degenerate stellar remnants anyway.

There are models where the expansion goes faster than exponential (only slightly faster now, with a mismatch that grows with time). In those models, the local group and other smaller things can get ripped apart. That’s what’s usually called the Big Rip.

## michaelbusch

November 17, 2013 at 5:06 pm (UTC -4) Link to this comment

As Mano said, that’s an analogy to describe the curvature of the space. The model Carroll is describing assumes zero curvature and flat, which would say that the universe is infinite. This is the best model currently available.

## Rob Grigjanis

November 17, 2013 at 5:08 pm (UTC -4) Link to this comment

The problem with talking about negative pressure is that many people confuse that with the idea of

lesspressure.If you blow up and seal a balloon, then increase the pressure in the region around it, the balloon will contract, because the pressure inside the balloon is less than that outside. Whence the idea that negative pressure should somehow cause contraction rather than expansion.

In this case, there is no ‘outside’, with any pressure (positive, or even less negative) to cause a contraction, and negative pressure is actually just another way of saying that dark energy density is constant (i.e. a property of space itself).

This is no more intuitive than the concept of negative mass.

## raven

November 17, 2013 at 5:17 pm (UTC -4) Link to this comment

Now I’m (more) confused.

1. If the fabric of space is expanded, what happens to the vacuum energy of space, which is nonzero. Shouldn’t it go down per unit of space?

2. If Dark Energy is an intrinsic property of space, and space is expanded, then it should go down too.

This sounds like quantum field theory. Dark Energy isn’t energy it is a field. And if I understood Carroll, he is saying that space is being created and with it, more Dark Energy.

## Rob Grigjanis

November 17, 2013 at 5:25 pm (UTC -4) Link to this comment

Yeah, still an open question (?).

Where w=P/ρ (P pressure, ρ density).

## F [i'm not here, i'm gone]

November 17, 2013 at 6:13 pm (UTC -4) Link to this comment

Well, really, it’s quite simple if you can drag anyone to a high school physics mindset: Acceleration is the rate of change. The word/concept “rate” is right in there. If they don’t understand this, they don’t understand acceleration in the first place.

## Gregory in Seattle

November 17, 2013 at 11:37 pm (UTC -4) Link to this comment

I remember two related problems in calculus, to the effect that if you increase the area of a circle at a constant rate, the circumference increases at a decreasing rate. If you increase the size of the circumference at a constant rate, then the area increases at an accelerating rate.

We are seeing the area of the universe (or whatever would be the 11 dimensional equivalent) increasing at an accelerating rate; ergo, the circumference — meaning the rate of expansion — is increasing at a constant rate.

Is that close enough?

## Gregory in Seattle

November 17, 2013 at 11:39 pm (UTC -4) Link to this comment

I just realized that I gave a false conclusion. But I assume that if both the area and circumference were increasing, we would be seeing predictable effects, which we are not seeing.

## Alex

November 18, 2013 at 4:34 am (UTC -4) Link to this comment

Are you sure that a simple Dark Energy dominated scenario with scale factor a = exp(H t) will lead to stuff being ripped apart in the far future? I think that the expansion forces acting on an object of a fixed size determined by other forces such as macroscopic objects will remain constant in the far future. You can always set a=1 for the present in this space. It’s just that non-gravitationally bound stuff will be out of sight after a while if I am not mistaken.

## Alex

November 18, 2013 at 4:37 am (UTC -4) Link to this comment

Yes, if you just count Dark Energy plus all the matter and radiation, I think it is fair to say that such energy is in effect being created. One can attempt to count the changing curvature of space as an increasingly negative contribution to energy (this is complicated by the fact that one cannot do that in a coordinate independent way – see Landau Lifshitz-Pseudotensor), and can even see the system as having constant zero total energy when including curvature.

## Alex

November 18, 2013 at 4:44 am (UTC -4) Link to this comment

Well yes and no. You can calculate the contributions to the vacuum energy density in quantum field theories such as the standard model, and the expression you will get is technically a quantum field – but then you take the expectation value, and you get out a number – one that is 120 orders of magnitude larger than what would be needed to explain the observed dark energy. So you have to choose the Einstein cosmological constant to cancel this humongous contribution down to the 120th digit. This is called the CC finetuning problem, and we’re at the heart of the problem – do we make a mistake when translating this quantum field operator into a number to plug into the Einstein equations, or is the universe really “finely tuned” to cancel the CC against the standard model contributions in this manner.

## Alex

November 18, 2013 at 4:52 am (UTC -4) Link to this comment

Well, there is the cosmological constant as a free parameter in the Einstein Equations. As I mentioned below, an equivalent kind of term is generated automatically in the standard model when one embeds it in Einsteinian Gravity as an effective theory that is valid up until near the Planck scale. The main problem is that these contributions to the Dark Energy seem to come out way to large. But when one adjusts them to the observed value using the cosmological constant paramter, the result explain perfectly well the observations, and they are there anyways in the theory – so it does not deserve the name kludge. From a modern perspective it’s just a free parameter in the theory, the value of which seems to be very finely tuned. There may be other contributions to dark energy beyond this basic one, but these would be until today observationally unnecessary complications added to the theory.

## Alex

November 18, 2013 at 5:31 am (UTC -4) Link to this comment

Yes, your analogy is not quite ok, because the number of dimensions does not change a linear expansion into an exponential one.

Carroll really only refers to how linear (distance) scales expand, by measuring how quickly far away objects seem to recede. The three-dimensional volume then increases with the third power of that, which is still an exponential increase, but with a factor 3 in the exponent

11D or 10D does not figure in this equation at all. If anything, the extra 6 or 7 dimensions of superstring/M-Theory would have to remain very constant in their volume, otherwise the laws of nature would change dramatically with time, in particular (and at the least) the strength of gravitation – something that is not observed.

## Mano Singham

November 18, 2013 at 7:55 am (UTC -4) Link to this comment

You are exactly right.

## Alex

November 18, 2013 at 8:20 am (UTC -4) Link to this comment

“the curvature of space-time” I mean, not the changing curvature of space

## Mano Singham

November 18, 2013 at 9:03 am (UTC -4) Link to this comment

What Carroll is talking about with ‘a’ is the scale favor (sometimes called R) which is the same in all directions. It simply tells you by how much all the scales should be multiplied, like the scale factor in maps.

## Rob Grigjanis

November 18, 2013 at 11:30 am (UTC -4) Link to this comment

Cool little interactive app allowing variation of six parameters (including dark energy) to try and match the observed Cosmic Microwave Background power spectrum (red curve);

http://map.gsfc.nasa.gov/resources/camb_tool/