Matter cools when universe expands. Where does that energy go to? I would expect that delta E = delta V (with some clear way to represent volume in Joules).
Shouldn't dark energy density also fall?
Shouldn't dark energy density also fall?
More precisely, the energy density of matter decreases as the universe expands.
> Where does that energy go to?
Stress-energy density is locally conserved; there is no energy being created or destroyed. In fact that local conservation of stress-energy density is what requires the energy density of matter (which in cosmology-speak means a perfect fluid with zero pressure) to decrease as the universe expands (as the cube of the scale factor).
> Shouldn't dark energy density also fall?
No, because dark energy, considered as a stress-energy density, includes negative pressure equal to minus the energy density, and the same local conservation of stress-energy density I referred to above requires that in this case, the energy density is constant in both space and time.
Note that the new findings described in the article amount to raising the possibility that what we thought was "dark energy", i.e., a cosmological constant with pressure exactly equal to minus the energy density (that is what w = -1, mentioned in the article, means), is in fact something else whose equation of state (relationship between pressure and energy density) can change over time, with pressure becoming less negative (w less negative than -1). If that is the case, the energy density would also be decreasing over time, though much more slowly than for ordinary matter.
That makes total sense!
Does this meak we know how much the total density of matter has to decrease in order for universe to expand one cubic meter? What's the energy equivalent of one new cubic meter of space, in Joules? Do we know that? Does it fit the observed matter density, with and without dark matter?
It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process.
It doesn't work that way. Remember that GR is a theory of spacetime geometry. When we say "the universe is expanding", that's really shorthand for "the spacetime geometry of the universe has a particular shape". It doesn't mean that the universe "adds cubic meters" over time.
There is certainly a relationship between the density of matter (or more generally stress-energy density) and the geometric property that informally we refer to as "the rate of expansion of the universe". The equations that express that relationship are the Friedmann equations, which are just the Einstein Field Equation, the central equation of GR, specialized to the kind of spacetime geometry that "expanding universe" refers to. But it's not really useful to think of those relationships as saying that if the matter density decreases by this much, it makes the universe expand that much.
> It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process.
No, that's not a good way to look at it.
A cosmological constant aka dark energy is best thought of as just an unusual form of perfect fluid whose pressure is minus its energy density. Then you just plug that into the Friedmann equations to get predictions for what we should expect to observe, such as "accelerating expansion".
You were talking about stress-energy tensor, and it did sound like density decrease is linked to the volume increase in a mathematical sense so that conservation happens. Now you say they are not related in that way. If the density decrease is not linked to the volume increase then you have to explain where that extra energy went.
"perfect fluid whose pressure is minus its energy density" does not make sense because you said it is expanding but keeping the same density. If a fluid is expanding but not becoming less dense, it wasn't a fluid in the first place.
Unfortunately what I can see is lack of understanding the mechanism and being able to productively reason about that, and stress-energy tensor is sufficiently complicated abstraction that one no longer feels the discomfort of not understanding.
Then you are disagreeing with our best current physical model of our universe, which does not say what you are saying.
> I'm not geting it out of this discussion.
You should be aware that General Relativity and modern cosmology are complex subjects, and cannot be understood all at once in the course of an Internet discussion. Do you know how long it took me to properly understand the model that I am giving you a very quick and abbreviated description of? Several decades. So if you're expecting a quick "sound bite" answer that will make sense to you, and you have no background whatever in those subjects, of course you are not going to get what you are looking for. I can't help that. All I can tell you is what our best current models say.
> You were talking about stress-energy tensor, and it did sound like density decrease is linked to the volume increase in a mathematical sense so that conservation happens. Now you say they are not related in that way.
No, that's not what I'm saying. What I'm saying is that the relationship is not a causal relationship, in which the density decrease causes the volume increase. It is just a relationship that is enforced by the overall relationship between the spacetime geometry and the stress-energy tensor. The general form of that relationship is the Einstein Field Equation, and the particular form that applies to our best current model of the universe is the Friedmann equations. Those equations most definitely do give a relationship between density decrease for matter and what you are calling "volume increase"--more precisely the rate of "volume increase" (but the term cosmologists actually use is "scale factor" and "rate of increase of the scale factor"), and that relationship most definitely does include a local conservation law for stress-energy. I apologize if that wasn't clear.
> "perfect fluid whose pressure is minus its energy density" does not make sense because you said it is expanding but keeping the same density. If a fluid is expanding but not becoming less dense, it wasn't a fluid in the first place.
I'm using "perfect fluid" here as a technical term for a particular form of the stress-energy tensor, where the only two things you need to specify are energy density and pressure. Terms like "matter" and "dark energy" are then just names for particular equations of state, i.e., particular relationships between energy density and pressure. "Matter" means pressure is zero. "Dark energy" means pressure is minus energy density. That is standard usage among cosmologists.
As for why the dark energy density stays the same as the universe expands, that's what the Friedmann equations say when pressure is minus energy density. If you don't like the term "perfect fluid" to describe such a thing, that's fine, call it something else if you like. (But don't expect cosmologists to go along with you.) The important point is the physics, not the words we use to describe it. The physics is what I said. You can check it for yourself if you like by looking up the Friedmann equations.
> what I can see is lack of understanding the mechanism
What I can see, and I can't avoid saying this bluntly, is someone who has no background in physics but still presumes to tell someone who does have such a background what they do and do not understand. Sorry, but you, and again I can't avoid saying this bluntly, simply don't know what you are talking about. I do know what I am talking about. I'm sorry that I can't convey what I know to you in a quick sound bite that will make sense to you, but that's beyond human powers. There's a reason that people spend years or decades studying these subjects, and there's a reason that even the basics are taught in university courses that take multiple semesters to complete and require textbooks and working problem sets and so on.
> What I'm saying is that the relationship is not a causal relationship, in which the density decrease causes the volume increase. It is just a relationship that is enforced by the overall relationship between the spacetime geometry and the stress-energy tensor.
I'm not even sure why focus on casuality of the event. I'm more interested in whether that stress-energy tensor is a tool which lets us reason about any interesting info, such as:
Can we imagine a noticeable area of space suddently becoming empty and devoid of matter - would it cause the inflation, as in elongation of paths between ourselves and some distant object with this area between us, to become faster? Slower? Just about the same?
When you talk about a "local conservation law", do you mean that there's math which makes the energy difference go away, and then inflation goes at the same rate regardless of whether energy-losing matter (such as light) is present in the expanding area or not? Because that just does not sound satisfactory.
Imagine driving over a $100 bill lying on the ground and once you've past it the bill is gone. You can reason that the bill wasn't significantly thick, and when you drove over it you created some tension and a measurable local depression, but once you went past the ground returned to the same level as it were. That is indeed true and scientifically sound. But where's that money now? That is a question that needs some answer.
Maybe it's now stuck to your wheel, maybe it's under a film of dust now, or somebody have pocketed it. But there has to be some answer.
Because your original question made it seem like you were thinking of the density decrease caused the volume increase. If you understand that that's not how it works, that's good.
> Can we imagine a noticeable area of space suddently becoming empty and devoid of matter
Note that this can't happen except by matter flowing out of the area. The matter can't just disappear. That is what the local conservation law for stress-energy says.
> would it cause the inflation, as in elongation of paths between ourselves and some distant object with this area between us, to become faster? Slower? Just about the same?
As I understand it, cosmologists are working on models in which the density of matter does vary from place to place as well as with time (although even phrasing it that way introduces technical issues that I won't go into here), because our observations seem to indicate that, for example, there is a "void" a billion light-years or more wide in our general vicinity, where the density is significantly lower. Note that this only applies to ordinary matter, not dark energy.
The general indications so far of those models, from what I understand, is that such "voids" result in a faster expansion in that area (though again I am ignoring significant technical issues with how this is phrased). However, this is still an open area of research, and the models become significantly more difficult to work with because you can't solve the equations analytically any more, the way you can when the density is constant everywhere in space. You have to do numerical simulations.
> When you talk about a "local conservation law", do you mean that there's math which makes the energy difference go away, and then inflation goes at the same rate regardless of whether energy-losing matter (such as light) is present in the expanding area or not?
I'm not sure what this means.
What the local conservation law says is that stress-energy cannot be created or destroyed; it can change form (for example, matter can transfer some of its stress-energy to radiation by emitting it), and it can flow between regions of spacetime, but the flow cannot have any sources or sinks. The complication is that the "flow" has to take into account the spacetime geometry, which affects how you "count" the flow. For example, if we consider an expanding universe containing just ordinary matter, the energy density decreases like the cube of the scale factor, but that is not a violation of the local conservation law, it's because of the local conservation law--the spacetime geometry is changing as well as the energy density, and the combination of the two changes keeps the local conservation law satisfied--in terms of the local conservation law, the "flow" is conserved, there are no sources or sinks, even though the energy density is changing.
This is one of those things that's really, really hard to explain in ordinary language. The mathematical statement is that the covariant divergence of the stress-energy tensor is zero. Physicists understand what that means and how to use it even if they can't express it very compactly in ordinary language.
That's exactly what I've feared. You just spent writing a full page of text how it takes several decades to understand the theory, then I ask a simplest of questions about it, one that any bright primary schooler will come up - and the understanding immediately implodes on itself because the answer is simply not there. All of these decades of studying led to a model that barely supports itself but cannot hold even lightest useful load.
Imagine how a person will study mechanical springs for several decades, then you ask them what happens if you add some load to the spring currently hanging idle, only to hear that it's an "open area of research". But it would probably go up. Something surely would.
I understand the idea of local conservation. Imagine an empty region of space where there's just light, and neutrinos, and some dust. Some time passed and some of that light (and neutrinos) lost energy due to red shift. Where did that energy went, stress-tensor or not? Where's the $100? Whose pocket does it line? What I'm hearing from you is "it can't go nowhere so it went somewhere" but that's not good enough. I suspected that already.
It can be that it's the same $100, they just worth much less than when they were printed because of all the other money which were in circulation between then and now. But that still needs to be described to the point.
No, the answer is there, but it's not simple. Again, you want a quick sound bite: yes or no to your question. And reality is not like that. Reality is not simple sound bites. Reality is complicated and it takes work to figure out what is really going on. That's why it takes years or decades to get a real understanding of any useful model of reality on the scale of the universe. That's why it takes years or decades to do research to expand the boundaries of our knowledge. You want me to just bypass all that and give you a simple answer. Sorry, no. There isn't one. That's not because scientists are stupid or because our models don't work. It's because you don't want to accept the actual cost of understanding them.
> Imagine how a person will study mechanical springs for several decades
But nobody does that. Physics students learn a simple model of how mechanical springs work in a lecture or two. Mechanical engineers learn more detailed models that work for things like designing car suspensions in maybe a semester. People might certainly work with mechanical springs for decades, but they won't spend that whole time just getting an understanding of our best current model of them. They will spend most of that time using the model that that already understand.
But the whole universe is not a mechanical spring. And learning our best current model of the whole universe is a lot harder than learning our best current model of a mechanical spring. So you are simply being unrealistic if you expect someone to explain the whole universe to you with the same amount of effort it would take to explain a mechanical spring.
> I understand the idea of local conservation.
No, you don't. You may think you do, but if you did, you would not even have to ask:
> Imagine an empty region of space where there's just light, and neutrinos, and some dust. Some time passed and some of that light (and neutrinos) lost energy due to red shift. Where did that energy went, stress-tensor or not?
Local conservation says no stress-energy went anywhere. The redshift due to the universe's expansion does not lose any stress-energy. Stress-energy is conserved.
A better question would be, if stress-energy is locally conserved, why is there a redshift as the universe expands? And the answer to that is that the local conservation law does not say the energy density stays the same. It says that stress-energy is not created or destroyed. But "stress-energy" is not the same as energy density. The density of stress-energy, for matter (or radiation, since you asked about light) is the same with the scale factor slightly smaller and the energy density slightly higher, as with the scale factor slightly larger and the energy density slightly smaller. That's what the equations tell us. (For dark energy, as I've said, they tell us that the energy density does stay the same as the universe expands. But that's only true for dark energy.) All of these statements are consequences of the Friedmann equations, or, if you want to look at it that way, of the relationship that is enforced by those equations between stress-energy and spacetime geometry.
That's about the best I can do at describing what the equations say in ordinary language. There's a reason why physicists do physics with math: because math is a much better tool for the job. I've already told you what math to look up if you want more information.
So you are saying, there is a semi-reversible process where energy and volume are correlated? That's what I've started with.
Should there actually be some specific amount of energy in place in order this density-to-scale transmutation to happen? What kinds of energy participate in it in our real world scenario? Does it depend on the specific local density (though I've already asked that)?
My original objection was to you thinking of it as a "process", or at least a process involving energy and volume. It's a relationship between stress-energy and spacetime geometry.
> Should there actually be some specific amount of energy in place in order this density-to-scale transmutation to happen?
There is no such "transmutation". That's not what's going on. Your questions aren't answerable because they are based on false premises.
At this point I've done my best to explain what is and isn't going on. All I can do is recommend reading more detailed treatments, which you can find in any cosmology textbook, or in briefer form in most GR textbooks. Sean Carroll's lecture notes on GR are available for free online [1], and Chapter 8 discusses the basics of our best current model of the universe in cosmology.