Is dark energy converted to gravitational potential energy?

Question

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?

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 --- ex-moderator kitten, Jan 08 '13 at 18:24
I am not sure if your quote "time-translational symmetry" holds in the framework of general relativity. — elcojon, Jan 08 '13 at 18:19
@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 08 '13 at 19:01
@Jerry For it to be hold, you need to check it in small volume of space and time only. — Earth is a Spoon, Jan 08 '13 at 19:11
@SachinShekhar: No. How you connect the small volumes is important, and in general, the time directions can get twisted up and confused with each other. The connection between the small volumes needs to respect the time coordinates of all of the observers. — Zo the Relativist, Jan 08 '13 at 19:19
@Jerry Say it complex in general situations, but not invalid. — Earth is a Spoon, Jan 08 '13 at 19:45
@SachinShekhar: there is no conserved energy without a global timelike killing vector. — Zo the Relativist, Jan 08 '13 at 19:56
@JerrySchirmer You don't have a tool to solve the problem, it doesn't mean energy isn't conserved. Its similar to a classical problem to solve which you've chosen wrong co-ordinate system. Due to insufficient data, you'll fail to solve the problem, but it doesn't mean problem is invalid. — Earth is a Spoon, Jan 10 '13 at 07:44
@SachinShekhar: Then walk me through the problem, using actual math, and show me the conserved energy in an open Mixmaster universe. — Zo the Relativist, Jan 10 '13 at 14:21

score 5 · Answer 1 · edited Dec 12 '21 at 13:52

There are a bunch of misconceptions in your question:

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
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.
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.
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.

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). — Earth is a Spoon, Jan 08 '13 at 19:21
@SachinShekhar: that's not at all what cosmic inflation says. — Zo the Relativist, Jan 08 '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. — Zo the Relativist, Jan 08 '13 at 19:29
You're just advocating Big Rip theory. My "Big Crunch" theory has more reputation.. :) — Earth is a Spoon, Jan 08 '13 at 19:32
@SachinShekhar: I'm doing neither. I'm explaining ordinary $\Lambda$CDM cosmology. — Zo the Relativist, Jan 08 '13 at 19:36
In Lambda-CDM model, dark energy is kept constant. It doesn't increase. — Earth is a Spoon, Jan 08 '13 at 19:41
@SachinShekhar: no, the dark energy DENSITY is kept constant, not the total amount of dark energy. — Zo the Relativist, Jan 08 '13 at 19:56

Is dark energy converted to gravitational potential energy?

1 Answers1