# Q: What is dark energy?

Physicist: The universe is expanding and the rate of that expansion is accelerating.  If the universe were full of only matter (both regular and dark) and energy, then we’d expect that the expansion would be slowing.  Dark energy is the thing that is responsible for that acceleration.  Now as for what exactly that thing is: we have interesting and vaguely informed guesses.

Back in the day Einstein came to a few realizations after he spent some time thinking about falling elevators and rockets.  This lead to a way of describing the nature of gravity (falling and whatnot) in terms of the geometry of spacetime and a relation between that geometry and the amount of matter and energy that’s around.  Einstein’s field equations can be used to describe how time and space are influenced by the presence of big chunks of matter like planets and stars, manages to explain/predict Mercury’s weird orbit and a bucket of other stuff, and has passed every test it’s been put to with flying colors.  That last bit is important: it’s easy to come up with crazy new theories, but hard to come up with theories that precisely predict results that were not previously understood.

Enter Friedmann, who happened to be thinking about the entire universe one day.  Einstein’s field equations related mass/energy with the shape of spacetime.  So, pondered Friedmann, what happens when you apply those equations to the universe as a whole?  First he assumed that space can expand or contract over time (why not?), then he threw that assumption at Einstein’s field equations to see if they’d stick.  Somewhat surprisingly, this is easier than it sounds.

Mr. Алекса́ндр Алекса́ндрович Фри́дман (Alexander Friedmann), a man who looks exactly like you’d hope he would.

On a totally over-the-top-large scale (billions of lightyears) the matter and energy of the universe is distributed roughly uniformly.  On this scale we describe the matter and energy in the universe as the “cosmological fluid”, because on the largest scales even the largest clumps of matter are as indistinguishable as atoms in water.  These “largest chunks” (as far as we know) are galactic super clusters; ours is about half a billion lightyears across and there are possibly many millions of super clusters in the observable universe.  And that’s only the observable universe.  Guessing the size of the entire universe based only on the part of it that we can see is like trying to guess the size of the Earth by standing in a featureless open field.

So you’re somewhere.  How big is it?

Words utterly fail when trying to describe how much “out there” is out there.  Point is: all that’s important for figuring out the behavior of the universe as a whole is the average density of matter and energy, which is roughly the same everywhere.  You don’t need to stress about every star and galaxy in the universe, or even about the size of the universe as a whole, any more than you need to stress about every grain of sand in a pile of sand.

When Friedmann said space can expand or contract over time he said it this way: $ds^2 = \left[a(t)\right]^2dx^2-c^2dt^2$.  That’s the spacetime interval (which is how distance is measured in spacetime) with the addition of a scaling term, a(t).  If a(t) doubles, that means that the distance between any two points in space has doubled.  So, if you figure out how a(t) changes over time, you can describe how the universe is expanding or contracting over time.  Incidentally, a(t) also describes the cosmological redshift of light; if a(t) doubles between when some light is emitted and absorbed, then the wavelength of that light (like the space it’s traveling through) will double and longer wavelengths mean redder.  The oldest light in the universe was emitted when a(t) was about 1100 times smaller than it is now.

It turns out (this is not obvious) that Einstein’s equations dictate that $a(t) = kt^\frac{2}{3(w+1)}$, where w is the weirdly named “equation of state” and k is a constant number.  $w=\frac{1}{3}$ and $a(t)\propto t^\frac{1}{2}$ for a universe filled with radiation (light, neutrinos, and matter moving near light speed).  $w=0$ and $a(t)\propto t^\frac{1}{3}$ for a universe filled with regular matter (including you, your stuff, basically everything else, and dark matter too).  In both of these cases the universe expands, and the rate of that expansion slows down, forever.

As space expands the density of matter and radiation decreases, because there’s more space for it to be spread out in.  But radiation not only gets more spread out, but redshifted as well and that means that the energy density of radiation drops faster than the energy density of ordinary matter.  So, we can expect that w, which describes a combination of both matter and radiation, should be somewhere in the range $0\le w\le \frac{1}{3}$.  Since the expansion of space decreases the energy density of radiation more than matter, over time w should drift closer to 0 as matter becomes more dominant.

The expansion of space decreases the energy density of matter by spreading it out and decreases the energy density of radiation by spreading it out as well as redshifting it. But the expansion of space doesn’t decrease the energy density of dark energy; instead it just seems to create more

But here’s the thing!  Since the late 90’s we’ve been able to show that the expansion of the universe is speeding up, not slowing down.  In order for that to happen the equation of state of the universe must be $w\le-\frac{1}{3}$.  This came as a bit of a shock to cosmologists.  But being brow-beaten by experiment and observation is what good science is all about.  Onward.

Upon closer examination of the expanding universe we find that including “stuff” with the equation of state w=-1 is a good fit.  This corresponds to a uniform negative energy with a constant density.  There are a couple of things about that which are… a little strange.  A constant density means that as space expands there’s more of this stuff around.  Matter and radiation are indeed being thinned out more and more by the expansion of the universe, but this very bizarre new stuff doesn’t get thinned out.  The fact that it has negative energy is just icing on the weirdness cake.

Not knowing what else to call it, physicists have dubbed this uniform, undiluting, negative-energy stuff “dark energy”.  That’s not to say that we have any idea what it is, but that’s no reason to not give something a name.  Unfortunately, dark energy and dark matter are difficult to study (hence the names) so it’s tricky to figure out exactly how much of each is around, but of the energy and matter around today roughly 75% is dark energy, 20% is dark matter, and 5% or less is regular matter.  Over time the percentage of dark energy should approach 100% as the expansion of space waters down all of the matter and radiation.

We can infer the existence of dark matter in large part because models of the universe that take it into account do a good job of describing the observed evolution of the universe, while models that don’t take dark energy into account do a terrible job.  Because the amount of dark energy seems to be proportional to the amount of space around, it seems fairly reasonable to say that dark energy is the “energy of empty space”.  What in the hell that’s supposed to mean is now a lively topic of discussion and debate.  There are a bunch of theorists and experimentalists running around trying to directly detect and/or describe dark energy, and with any luck they just might do it.

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### 28 Responses to Q: What is dark energy?

1. Tommy says:

Here’s the thing! If the cosmological model fails due to observed evidence then you don’t invent unobserved stuff to cover up the failings of your theory. You admit the theory is wrong and look for the truth instead. That’s good science. You’re going to need more than luck to find stuff that doesn’t exist.

2. Very nice. Short and sweet.

3. Berndt Barkholz says:

Tommy is right !!

It’s a very naive thought that “nothingness” is increasing and it’s outrageous that this stupid idea is “sold” as knowledge…

4. In GR space is not nothing. It carries energy, e.g., gravitational waves recently seen.

5. Peter von zur Muehlen says:

Ungh’ Curse my inability to read math equations and make heads or tales of them. I really want to understand this better.
I have some things to say about this maybe but first I need to clarify some things. Firstly the difference between the universe expanding because of the big bang as opposed to the idea that it is expanding because the space between things is growing. How do we tell the difference between that? for instance if two cars race away in opposite directions then the distance between does appear to grow, but we would never say they are moving because the space between them is growing. However, if two people were standing at the center of a football field upon a very large sheet that was all crumpled up in the middle and the sheet began to be pulled apart thus bring the people with it but the where actually standing still relative to the patch of sheet they were one, then in that case we would say that they are moving apart because the sheet is moving/growing in the middle and they are just going along for the ride. Now i figure that if space is expanding and not just the stuff in the space moving relative to the other stuff then we have actually a combination of the space moving the things in the space while the things themselves are also moving. relative to each other and to the space. The idea that space itself can expand beyond the idea that things in space move apart, I think lends something to the notion of absolute space, Like something you can impose a grid on, except that the in this idea the grid itself is being stretch or filled in with more grid. At this point I am afraid I might have taken the brown acid and should search for help.

I also imagine an analogy of those conveyor walkways they have at airports. For instance. if the walkway is moving on down the corridor in one direction, and someone on that walkway is also walking in the same direction that it is moving his walking speed is accelerated away from someone standing still or walking in the opposite direction more than would be for someone walking away but not on the conveyor walkway.

So the idea of dark energy is inferred from observations and interpretations of those observations. It could be a case in which the interpretation is just incorrect and we don’t understand the data or have observed it in error somehow making it erroneous. Maybe that is redundant.

Here is a theory. if the various billions of galaxies are moving farther apart from each other due to simple expansion, ever outward from the center of the big bang, then wouldn’t that mean that the gravitational pull between all those massive objects is lessening as the move apart? Could the dark energy be the result of the energy conservation of that gravity? Like the opposite of the acceleration an object falling picks up as it moves through the time shells getting closer to the center of gravity. The overall energy has to stay the same right?

If that is true, and we know that gravity can lens and bend light light, maybe dark matter is also just the effect of that same gravity, or the energy from the gravity, just sort of piling up in open space.

Maybe that is crazy and makes no sense. I wish i could understand the math, without the math I am left with trying to visualise the information into some analogous form, and I may be completely missing the boat.

On the subject of dark matter. It seems like it might need a better name. Because when you say dark matter I think most people visualize something like a lump of coal or volcanic rock. But from what I am reading Dark matter bends light but it does not block light. So really it is more like invisible matter. Though why do we think that dark matter and dark energy are different from each other? Back to my stretching a bunched up sheet apart analogy, if space can expand, like just out of nowhere grow, then maybe it can also get bunched up, and that is somehow bending light. Perhaps that makes less sense than the other thing I said.

6. There are only 3 other things in the universe that reliably increase over time: information, entropy, and the average complexity of living organisms. What if dark energy is basically information, and as time passes it increases the space, i.e. the number of alternate paths anything can take (and thus dark energy), and so provides variations in complex chemical systems that can be tested by selection and end up with life and intelligence? So time is just the making room for information, and the plot thickens.

7. Tim says:

Einstein was so hella smart

8. PJ London says:

The London Hypothesis : “The universe is expanding because Infinity Sucks!”

9. Bert Plante says:

Being an infinitist, I wonder about an external “pull” from our big bang.

10. IF YOU ARE CORRECT THEN YOU SHOULD BE ABLE TO DESCRIBE HOW AND WHERE THE SPACE ENDS.

11. Grant Anderson says:

So, is “Dark Matter” and “Dark Energy” touching my nose right now???
If not, where is this invisible “event horizon”???

12. George D Conger says:

Space and time are two totally different things physically and can not be joined.
However, acceleration can make it appear that space is contracting or that time is dilating in two frames of reference. Now, if you hypothesize a fixed external observer, you find the discrepancies disappear.

The growing number of “skeptics” of BBT and “inflation of space” etc are growing more rapidly. Why not explain all this in this forum?
G

13. So, is “Dark Matter” and “Dark Energy” touching my nose right now???
If not, where is this invisible “event horizon”???

`Yes, no

14. ENGLISH BOB says:

Can we have a proper question ? Like, How do you calculate how much Matter there is in the (whole universe) and not just the bit we know about. Without using a smoke screen of incomprehensible mathematical gobbledygook ? With regard to dark energy/matter. Tom is correct .

15. Berndt Barkholz says:

We simply cannot calculate the total mass of the universe ! All we can do is making estimations based on estimations. We BELIEVE that our theories are correct, we do not know that they are !

16. “Like, How do you calculate how much Matter there is in the (whole universe) and not just the bit we know about”

The universe is infinite so ‘how much in the whole universe’ makes no sense. Name a number, any number and it’s bigger than that. Pick on a bigger one and it’s bigger than that. You can keep on forever, if you live that long.

Only density makes sense. We can only give a total for some finite piece like the light cone. Or bigger. Pick a size as big as you like.

-Traruh

17. Berndt Barkholz says:

True Traruh, only density makes sense. The universe has a certain average density and this density only (!) can be the cause for the observed red-shift… Big-Bang and the expansion of the universe is not even a fairy tale… (in the same sense as Pauli’s “not even wrong”)

18. Bert Plante says:

Is your universe limited to our big bang?

19. Robert says:

With all the energy generated from the thermal nuclear reactions of billions of stars that emit solar wind and neutrinos, and the extremely week gravitational forces, have any thing to do with the acceleration of the universe.

20. ENGLISH BOB says:

Do we know whether the expansion of the universe, has always been ecelerating from the year dot. ie; That it started off in slow motion and has gradually been speeding up. Just getting faster and faster?

21. ENGLISH BOB says:

Density of the known universe is just another guess. BUT assuming you’re right. what about the stuff we don’t know about ? It could be huge, in comparison to what we do know and it could be empty or stuffed to the rafters with stuff. Either way you’re density will need adjusting. Every speck of dust or grain of sand has to be taken into account. And that’s impossible. It can’t be dun. Good luck trying.

22. >Every speck of dust or grain of sand has to be taken into account

>Really? Do you need to account for every ‘grain’ to get the density of the sand in a bottle?

You can ‘sample’ it! If you were a bug living in he sand you’d sample around you. You would need a ‘theory’ to estimate the density beyond the region you could explore.

We have a theory. The bug I would guess does not and is not much interested anyhow.

23. ENGLISH BOB says:

This bug is very interested. The sand in the bottle is a closed system. The universe is not. The bottle may have been dropped in a rainforest or out in the middle of the ocean. What’s outside the bottle really does matter. We have lots of theories, unfortunately we need facts (The Truth) and that’s still not possible. Nice try.

24. Bob, =a really big bottle… )=-

=Traruh

25. ENGLISH BOB says:

I think we are on the same wave length =Traruh, But I just can’t resist playing devils advocate. All the best, BOB.

26. Eyesinthedrk says:

We will never find dark mater or dark energy, mainly because it doesn’t exist. The scientific community is assuming this is the work of something complicated so that’s what they are looking for. The answer is simple and right in front of our eyes. That answer is Justin Bieber’s music. The only thing in the universe so repulsive that even space itself is expanding in an attempt to get away from it. Have your peers plug the Belieber Effect into their models and see what happens.

27. Mk says:

Could you explain a little about the way the energy density can be changing but the laws of thermodynamics can still hold? Could the notion of energy be redefined where the energy density is conserved but energy is not conserved?

Also if dark energy is negative and it is 75% of total energy vs. 25% positive energy in the universe then does this mean there’s a net negative 50% energy in the universe?

Lastly what are some of the leading theories out there to explain dark energy and do they make any testable predictions? I’ve heard of it being energy of the vacuum so if it is negative does this mean something like there’s a cost in energy for things that we know of like particles to exist?

28. Psymanonono says:

The answer to this question is closer than we think. there is no need to calculate the density of matter when there are random holes (black holes) in them that absorve various amounts of that same matter and spit it out somewhere else or makes it dissapear. The density of matter is what it is. figuring out what it’s all made of doesnt answer the real question after all. And from our perspective that question is where the hell first 3 dimensional matter came from and why do we apperantly have the ability to figure out and wonder about more than we can experience in this so called 3d life.

When you have solved those questions the universe becomes the simplest thing you ever imagined.