> I don't agree with you.

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.