Exploring Negative Energy Density and its Impact on Universe Models

[Arman777]

There are some universe models where $\Lambda < 0$. In this case, the energy density of the dark-energy becomes negative. At this point, does it make sense to talk about "negative dark energy density"? Or is it possible to think of this energy as curvature on space-time? Such that, $\Lambda < 0$ will imply a negative curvature and $\Lambda > 0$ positive one.

For instance if we have a only matter with $\Omega_m = 0.3$ the universe will have negative curvature with $\Omega_{\kappa} = 0.7$.

When we add positive dark energy such that $\Omega_{\Lambda} = 0.7$ we would have $\Omega_{\kappa} = 0$.

If we add negative dark energy such that $\Omega_{\Lambda} = -0.7$, we would have $\Omega_{\kappa} = 1.4$

So adding positive energy density increases the curvature.

In other words is there a something call "negative" energy density ? or
Does all negative energy densities are thought in terms of the curvature effects on space-time?

 

[PeterDonis]

In this case, the energy density of the dark-energy becomes negative. At this point, does it make sense to talk about "negative dark energy density"? Or is it possible to think of this energy as curvature on space-time?

These are not two different things. They're just two different ways of talking in ordinary language about the same thing.

So adding positive energy density increases the curvature.

The curvature in this case is curvature of space, not spacetime.

 

[Arman777]

These are not two different things. They're just two different ways of talking in ordinary language about the same thing.
The curvature in this case is curvature of space, not spacetime.

I see your point. It seems interesting to me because in an article that I am reading it is claimed that the dark energy changes its energy density from negative to positive at $z=z_{transition}$. So they claim that, at $z_{trans} = 2.37$, $\Omega_{\Lambda} = -0.7$ becomes $\Omega_{\Lambda} = 0.7$ instantly.

If we can describe the energy densities in terms of the curvature, and change in the curvature travels by the speed of light (via gravitational waves), then how can this sudden change in the dark energy occur?

I am referring to this article:
https://ui.adsabs.harvard.edu/abs/2020PhRvD.101f3528A/abstract

The article explains the consequences of this sudden change, but it does not explain how. I believe there's something wrong with this idea.

There's also another problem. If we assume the universe is flat, it should be always flat. Then, how DE energy density can change suddenly without altering the "flatness" of the universe.

 

[PeterDonis]

how can this sudden change in the dark energy occur?

I haven't read the article in detail, but I would guess that they don't intend a literally instantaneous transition, just one that is very fast on cosmological time scales, but still continuous, not a discrete jump.

On a quick glance the article looks like fairly advanced speculation which probably won't be easily intelligible to someone not already familiar with the many references it gives.

If we assume the universe is flat, it should be always flat.

Again, "flat" here is referring to the curvature of space, not spacetime--more precisely, the curvature of space as seen by comoving observers. It is true that the standard FRW models which are spatially flat are spatially flat everywhere. But that is way short of a general proof that any spatially flat model must be spatially flat everywhere.

 

[Arman777]

I haven't read the article in detail, but I would guess that they don't intend an instantaneous transition, just one that is very fast on cosmological time scales, but still continuous, not a discrete jump.

For the given values it seems instantaneous. Equations also contain a sgn function, it must be instantaneous. It cannot be also continuous otherwise the $\Omega_{\Lambda}$ hits $0$ at some point which is also problematic.

On a quick glance the article looks like fairly advanced speculation which probably won't be easily intelligible to someone not already familiar with the many references it gives.

Well yes, it's an interesting idea. Maybe I am missing something.

 

[Arman777]

Again, "flat" here is referring to the curvature of space, not spacetime--more precisely, the curvature of space as seen by comoving observers. It is true that the standard FRW models which are spatially flat are spatially flat everywhere. But that is way short of a general proof that any spatially flat model must be spatially flat everywhere.

Hmm, so you are saying that the change in the energy density of the universe does not produce gravitational waves since the curvature $\Omega_{\kappa}$ measures the curvature of space and not space-time?

In other words, the curvature of space changes but this process does not produce any gravitational waves, since GW travels in space-time.

But that is way short of a general proof that any spatially flat model must be spatially flat everywhere.

There's also local flatness yes..

 

[PeterDonis]

so you are saying that the change in the energy density of the universe does not produce gravitational waves

There are no gravitational waves at all in any of the spacetimes under consideration; they have too high a degree of symmetry. That is true regardless of how the energy density behaves.

since the curvature $\Omega_k$ measures the curvature of space and not space-time?

No, that has nothing to do with the lack of gravitational waves in these spacetimes. See above.

In other words, the curvature of space changes but this process does not produce any gravitational waves, since GW travels in space-time.

No. See above.

There's also local flatness

That has nothing to do with the kind of flatness denoted by $\Omega_k = 0$.

You appear to be trying to apply your untrained intuitions to a highly advanced topic where you would need highly trained intuitions instead. That's not a good strategy.

 

[Arman777]

There are no gravitational waves at all in any of the spacetimes under consideration; they have too high a degree of symmetry.

I did not understand this.

You appear to be trying to apply your untrained intuitions to a highly advanced topic where you would need highly trained intuitions instead. That's not a good strategy.

Yes that is kind of true. Okay so let us forget about graviational waves and curvature etc.

What are your thoughts about this part of my question

For the given values it seems instantaneous. Equations also contain a sign function, it must be instantaneous. It cannot be also continuous otherwise the $\Omega_{\Lambda}$ hits $0$ at some point which is also problematic.

There are 4 authors of this article so I am sure that there's nothing wrong with the theory. But my question is more about how than why. Do you have any opinion about it ? or is it too technical for me to understand?

My mind cannot grasp the idea of the change in the DE density so "suddenly". What are your thoughts about the theory itself? Or particular in this topic?

I'll have a chance to meet one of the authors of this article in the coming weeks, and I am going to ask him as well.

 

[PeterDonis]

What are your thoughts about this part of my question

The sign function, as far as I can tell, only appears in the limit $\lambda \rightarrow \infty$, which is an unrealistic idealization anyway. I don't think the paper is trying to claim that this can actually occur in the real universe. They are just using it as a convenient simplification for a heuristic description.

What are your thoughts about the theory itself?

I'm not familiar enough with the kind of model they are using (which, as I said, seems to be a fairly advanced speculation discussed in many references) to have a useful opinion.

I'll have a chance to meet one of the authors of this article in the coming weeks, and I am going to ask him as well.

I'll be interested to see what he says.

 

[Arman777]

The sign function, as far as I can tell, only appears in the limit $\lambda \rightarrow \infty$, which is an unrealistic idealization anyway. I don't think the paper is trying to claim that this can actually occur in the real universe. They are just using it as a convenient simplification for a heuristic description.
I'm not familiar enough with the kind of model they are using (which, as I said, seems to be a fairly advanced speculation discussed in many references) to have a useful opinion.
I'll be interested to see what he says.

I can share his answer. Thanks for sharing your opinion about it.