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The equation of state for a perfect fluid is that $p=\omega \rho c^{2}$, where $p$ is the pressure, $\rho$ is the density, $c$ is the vacuum speed of light, and $\omega$ is called the equation of state parameter. $\omega$ may be constant or varying in time. I'm looking for broad answers (and references if possible) to the following:

  • Why is it important that the equation of state parameter of dark energy is measured?
  • What will it tell us?
  • What are the implications?
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Do you want an answer specific for dark-energy? As far as I know, equation of state parameter for simple energy and matter would be equally important and significant in their implications. –  Cheeku Mar 9 '13 at 16:00
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Your comment makes no sense. –  user12345 Mar 12 '13 at 18:57
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4 Answers

It's Einstein vs. Bohr all over again. If w is exactly -1 and doesn't change, then Einstein's cosmological constant is the correct explanation. If it's anything else, then there is some other explanation, most likely a quantum field. Google or wiki "Quintessence" for one of the leading contenders. This time, so far, Einstein seems to be winning, but the quantum gang is not yet ready to accept this.

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Yes, measuring $\omega = -1$ will tell us that the dark energy is a 'cosmological constant' but what does that tell us? –  user12345 Mar 7 '13 at 7:57
    
Maybe it gives us a hint which way to go in unifying GR and QM into Quantum Gravity? A bigger news would be the discovery of some deviation from GR which we could then further study. That would be very informative. –  Jim Graber Mar 7 '13 at 10:34
    
You have a point about the cosmological constant, but I don't think this has anything to do with Bohr. And there's nothing like the quantum gang "not accepting" Einstein. GR is after all an effective theory at long distances, whose microscopic details we still don't understand. –  Siva Mar 15 '13 at 5:07
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It gives us a clue about the future of the universe, since dark energy is the dominant form of energy in the universe and will become even more dominant in the future. The precise value of $w$ will therefore have a significant effect on the future expansion profile.

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This is from a blog post I wrote on the subject, Dark Energy and the Cosmic Horizon. The value of $w$ has a significant effect on the behavior of the cosmic horizon in the far future - for $w = -1$ it remains a constant size, for $w > -1$ it grows without bound over time, and for $w < -1$ it shrinks. In the latter case, the scale factor goes to infinity in a finite time - a scenario called the Big Rip.

More generally, measuring dark energy in all the ways we can think of should give us clues about what the heck the stuff is. Don't forget that "dark" just means "we know it's there, but don't ask us to explain it". The fact that it's the dominant form of energy in the universe and we have no idea what it is is plenty reason to be curious!

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"measuring dark energy in all the ways we can think of should give us clues about what the heck the stuff is" This. Can't get serious about understanding the physics of the stuff until our knowledge is not limited to what it isn't. Dark sector physics is just getting started. –  dmckee Mar 9 '13 at 22:38
    
Interesting. Yes, I was looking for "measuring dark energy in all the ways we can think of should give us clues about what the heck the stuff is" - but in a more fleshed out answer, perhaps examples and references. In that case, I'd gladly award the bounty to whoever makes the answer. –  user12345 Mar 12 '13 at 19:04
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Whoever downvoted, would you mind explaining, in the interests of improving this answer? –  Nathan Reed Mar 12 '13 at 22:10
    
@NathanReed Two-thirds of your answer is just about what the Universe will do in the VERY far future (from your graph - at least 50 billion years) - this would appear essentially irrelevant. The comment on "measuring dark energy in all the ways we can think of should give us clues about what the heck the stuff is" is what I'm looking for but you give absolutely no statements/ references of 'how exactly?' –  user12345 Mar 16 '13 at 13:54
    
@user16307 You asked "what will it tell us" and "what are the implications". In my answer is something it will tell us and the implications of that. If you consider this "essentially irrelevant", well, I can't control that, nor can I control what you do or don't consider to be an "important" reason for the equation of state parameter to be measured. I wrote about an aspect of dark energy that seems interesting and important to me, and gave you a reference to my blog post to read more if you wanted. –  Nathan Reed Mar 16 '13 at 20:04
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@NathanReed gives a good explanation of some implications. I'll try to better address the other aspects.

Like you've mentioned in the question $\omega$ is some parameter to effectively characterize and model the thermodynamic properties of some stuff (dark energy in this case). It doesn't tell you what that stuff is actually made up of. We have many different models for what microscopic theory explains dark energy, and they predict different values for $\omega$. So measuring $\omega$ gives us a way to test those microscopic theories. For eg: If dark energy is described by a cosmological constant, then $\omega = -1$. If instead it consisted of (say) scalar or tensor fields, or some combination, then depending on the microscopic details of the theory, different values of $\omega$ will be predicted for dark energy.

Effective combined $omega$ for all the stuff in the universe (together) is a weighted combination of contributions from things like slow moving matter (both baryonic and dark) with $\omega=0$, ultrarelativistic matter with $\omega = \frac{1}{3}$ and dark energy (presumably $\omega \sim -1$). So an accurate measurement of $\omega$ will also give us a clue to the relative abundances of different kinds of stuff.

References

  1. https://en.wikipedia.org/wiki/Equation_of_state_%28cosmology%29
  2. http://www.scholarpedia.org/article/Dark_energy and further references listed there.
  3. Standard textbooks on large-scale cosmology shoud talk about this. You could look at (say) Weinberg's text.
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References:

http://wfirst.gsfc.nasa.gov/science/DETF_Report.pdf

http://arxiv.org/abs/1211.0310

http://sci.esa.int/science-e/www/area/index.cfm?fareaid=102

You asked for good references. Here are three. I don’t know your level of sophistication, but these are written for a funder’s point of view and are hence easier to understand. But the many references contained therein will give you a more detailed science approach if that is what you are interested in.

The first reference, from around 2005, is still regarded as the definitive statement of the problem from a US point of view. The second, from 2012, is a very good update from one specific project perspective (LSST). The third, a website, gives you the current take from the leading European related space project (Euclid).

You also asked why this is important. Everyone seems to agree that the dark energy is the most massive unsolved problem in cosmology. Let me quote from the top of the third reference:

“Theme: How did the Universe originate and what is it made of?”

Is that important enough for you? (Grin)

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As evidenced by the millions of Euros and dollars being spent, a whole lot of very smart and very serious people believe that this is a very important issue. The majority of them and of the related science community seems to expect that they will find something other than Wo = -1 and Wa = 0. My own hunch (which is worth absolutely nothing, not even $.02, and certainly no where near the cost of a flagship satellite mission) is that they will be disappointed. –  Jim Graber Mar 15 '13 at 17:41
    
Homework: Calculate how much the average US citizen and the average European citizen have spent and will spend on measuring W(t) to great precision. (Another grin) –  Jim Graber Mar 15 '13 at 17:42
    
Don't get me wrong, I'm not saying that it's not important. I don't need to be convinced about the funding. I am looking for the gory details on what exactly we can say about DE from measuring $\omega$. –  user12345 Mar 16 '13 at 13:56
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