Thursday, March 11, 2010

Dark Energy As A Prediction Of General Relativity.

(This is the second post on my dark energy series.)

In physics, we have learned its best to write down theories in terms of Lagrangians or actions.  (See the GR one below).  We have also learned that you need to include every term in your Lagrangian consistant with the underlying symmetries of the theory.

For example, take the standard model of particle physics.  You take the known symmetries we observe in nature, SU(3)xSU(2)xU(1), and then write down every term comparable with this symmetry.  This is very important.  If you forget a term you get the wrong answer.

With this in mind, why would general relativity (GR) be any different?  Why would we not demand an action containing every term compatible with the underlying symmetries?

Going back to our paper we read:
The most general low-energy second order action for the gravitational field, invariant under the relevant symmetry (diffeomorphisms) is
And what is lambda?  Why, it is the cosmological constant.  The fact that you can add a constant means that you should expect too for the reasons stated above.

GR without a cosmological constant is what needs explaining, not GR with one.  And a cosmological constant gives rise to an effect completely akin to dark energy.  For this reason, a dark energy like effect should be thought of as a prediction of GR.
From the point of view of classical general relativity, the presence of the cosmological term is natural and a vanishing value for λ would be more puzzling than a finite value: the theory naturally depends on two constants; the fact that some old textbooks only stress one (G) is only due to the fact that the effects of the second (λ) had not been observed yet.
So if you accept GR, in a sense you should expect to see something resembling dark energy. Furthermore,
In gravitational physics there is nothing mysterious in the cosmological constant. At least nothing more mysterious than the Maxwell equations, the Yang-Mills equations, the Dirac equation, or the Standard Model equations. These equations contain constants whose values we are not able to compute from first principles. The cosmological constant is in no sense more of a “mystery” than any other among the numerous constants in our fundamental theories.
How true.  We play this same game with every other theory: we add every term, constant etc.., compatible with the underlying symmetries and and never complain.  Why complain that we would need to add one to GR?

Physically this is like asking: why are we therefore so surprised to see dark energy?


  1. Furthermore:

    Take for example Newton's gravitational constant G. We have no reason to put it into the theory other than on dimensional grounds. Why are the "we need every consistent term in the Lagrangian" grounds less compelling?

    Also, we can not discern G's value as positive, negative, big or small from the theory. We have to look toward experiment to discern it's true value.

    So statements like this: "Can you give me a single reason why that constant should be constant? or why it's not negative?" seem a little prejudice.

    Can you give me a single reason, without preforming an experiment, why G should be constant or not negative? It seems like lambda is being unfairly treated.

    Now you may say, but we can calculate it using QFT, at it's off. That critique will be covered in a later post.

  2. Joe,

    I say this in good fun, but I it's easy to make a "prediction" from theory to agree with an observation that has already been made.

    The real issue is that dark energy is so different from the material that we interact with in any other branch of physics and it's brand new. That means that (a) there is some skepticism (one prominent cosmologist at CU calls it "the aether of our time") and (b) people want to understand it the same way that we understand gravity, E&M, or neutrinos. I think the skepticism is healthy - if your theory requires something like negative pressure that has never been observed before, then we better make sure it's right.

    It may turn out the the cosmological constant is like Netwon's gravitational constant, the fundamental unit of charge, or Plank's constant - it simply is. But those are very rare and before we canonize lambda, we better take a closer look at it.

  3. "I say this in good fun, but I it's easy to make a "prediction" from theory to agree with an observation that has already been made."

    Nick, cosmologists were saying there should be a cosmological constant that should only be zero if there is some symmetry we don't understand for decades before it was measured.

    Meaning, this was predicted before experiments. Just nobody knew what value it took on. *This was the point in trying to measure it in the first place*. People know it should be there unless an un-understood symmetry was setting it to zero.

    So how in the world can you claim the prediction comes after the observation? Well before any observation people were saying it may be there, but admittedly they weren't sure and they knew if it was there it had to be small.

  4. "one prominent cosmologist at CU calls it "the aether of our time"

    Again, talk about being unfair in a comparison.

    People tried at length to detect aether and never found it. I am confused why you keep putting dark energy in the same camp as aether.

    Aether was never detected and it's predictions were all false.

    Dark energy has been detected and predictions it makes on models are correct?

    How is it possible to compare these two?

  5. But, I admit dark energy is not as well understood as things like gravity.

    I really do appreciate your comments as these are very common claims. But I do think they are unfair, which is the whole point of this series.

  6. Joe,

    I have to somewhat agree with Nick on this. From a formula standpoint, yes, dark energy is not so suprising. But from a "wrap my mind around what it is" stand point, it seems very suprising.

    GR may have predicted the existence dark energy, but it doesn't seem like it really tells us "what it is." Especially to a layman like myself. It seems rather forboding and mysterious.

    Perhaps we could say the same thing about gravity. But I just don't feel the same way about gravity because I interact with it regularly. Also, curvature in space doesn't seem all that mysterious, so I have a warm fuzzy feeling that I "understand gravity" at least until we get to the quantum level.

  7. Sorry, I couldn't get it to work. I'm the Anonymous above. (Bruce Nielson)

  8. Anonymous(Bruce Nielson),

    Thank you for your comment and I should say it is wise to agree with Nick as he is very smart and cautious the way a scientist should be cautious and I am too much of a loose cannon.

    How, I think eventually we will finally realize dark energy is a cosmological constant and that all the fuss over this being "sooo mysterious" will turn out to have been blown out of proportion.

    That said, we will see.

  9. I should also at this apologize to Nick since:

    1. I am a loose cannon sometimes.
    2. He is wise to be cautious.
    3. I am way more aggressive with his comments than anyone else's. (This is psychological as I spent years arguing physics with Nick at BYU and it just seems natural. :))


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