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Dark Energy is basically doing work against gravity to accelerate the expansion of universe. So, for time-translational symmetry to be hold, dark energy must be converted to gravitational potential energy. I don't think, it can violate critical mass condition required for Cosmic Inflation because gravitational potential energy also have effective mass (stress-energy tensor).

But, here's a fact about Dark Energy: Its Cosmological Constant model refers to a constant energy density filling space homogenously. While its Quintessence model exists, Cosmological Model remains unchallenged.

Where's the catch? Is dark energy converted to gravitational potential energy? Or, my reasoning has a loophole?

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I am not sure if your quote "time-translational symmetry" holds in the framework of general relativity. –  elcojon Jan 8 '13 at 18:19
    
It may be a little early to identify dark energy with a Einsteinian cosmological constant: while that identification is often used as the least hypothesis it is also what the next generation deep field telescopes are being designed to investigate. –  dmckee Jan 8 '13 at 18:24
    
1) It does not hold in general, in general relativity. Most realisitic cosmological models, in fact, have a "Preferred cosmological time" 2) A cosmological constant does not violate time translation symmetry. –  Jerry Schirmer Jan 8 '13 at 18:48
    
@SachinShekhar: That was also my first intention. But I could not find the comment button. So I rather preferred to write in the 'wrong' box, then leave this comment only to myself. –  elcojon Jan 8 '13 at 19:01
    
@Jerry For it to be hold, you need to check it in small volume of space and time only. –  Sachin Shekhar Jan 8 '13 at 19:11
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2 Answers 2

There are a bunch of misconceptions in your question:

1) General relativity is a field theory, first and foremost. While we can certainly talk about energies and such in this contect, it is not the most natural language for the theory, which is phrased in terms of the fields themselves--where is the potential energy in an electromagnetic field distribution? Where is the kinetic energy? They're tied together a lot. The natural thing in these theories is the fields and their field equations. In this context, dark energy, expressed as a cosmological constant, is one of the simplest possible formulations

2) In general relativity in particular, the notion of global conservation of energy is a very tricky one. This is because there is no natural time coordinate to use to find the congugate energy. There is a special subclass of solutions, those of asymptotically flat spacetime, where there IS a notion of global conservation of energy. Simple examples of these solutions would be those describing isolated black holes. Unfortunately, most cosmological models are NOT asymptotically flat. So talking about the conservation of the TOTAL energy of the spacetime is meaningless.

3)Dark energy, in a simple energy analogy, would probably be better thought of as adding more negative potential energy--it certainly is the case that, as the universe expands, we're getting more dark energy, not less. So, thinking of this in terms of dark energy getting converted to KE is an incorrect way of viewing the model.

4)People believe the model because it is the simplest model that fits the data. There are simple extensions that add complexity that would satisify some of your concerns. It is also still possible, though increasingly less probable, that we live in the universe described by one of the void models.

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If we are getting more dark energy as universe expands, there'd be no point of return. But, cosmic inflation says that there's 50% probability that universe would contract (mirror reverse of current expansion). Without increased gravitational potential, this isn't possible too (big space to collapse). –  Sachin Shekhar Jan 8 '13 at 19:21
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@SachinShekhar: that's not at all what cosmic inflation says. –  Jerry Schirmer Jan 8 '13 at 19:24
    
And what I'm really saying is that freshman year conservation of energy is a really bad way to think about this problem. Isolating kinetic and potential energy in any rigorous way is next to impossible in full general relativity. –  Jerry Schirmer Jan 8 '13 at 19:29
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@SachinShekhar: I'm doing neither. I'm explaining ordinary $\Lambda$CDM cosmology. –  Jerry Schirmer Jan 8 '13 at 19:36
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@SachinShekhar: no, the dark energy DENSITY is kept constant, not the total amount of dark energy. –  Jerry Schirmer Jan 8 '13 at 19:56
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Energy cannot be created or destroyed, it only changes form. That's a pretty solid law to dismiss by saying that the total amount of dark energy is increasing. Where does it come from?

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Welcome to universe which is way beyond our common sense. –  Sachin Shekhar Mar 29 at 2:24
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protected by Qmechanic Jun 15 at 17:23

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