Hi Hossein

Eistein's general relativity is a classical model. Gravity was not quantized yet. At least there is no definitive model for the quantization of gravity. So, the answer is simply no.

Dear Cesar

I agree with you, thank you.

It is worth noting when the Einstein cosmological model (also the Friedman model) was presented that quantum mechanics was not so much development.

Modern physics is included the mass-energy equivalence due to relativity. And in modern physics, the old concept of force was replaced by the exchange discrete amounts of energy. So if we want to have a real understanding of the cosmos and present a real cosmological model, then we must generalize the mass-energy conservation law to the fundamental forces carriers (the discrete amounts of energy that are transmitted by the bosons). There is another problem in modern physics that relativity had not arisen and answer to it, and it is the minimum of speed.

The limitation of the minimum speed

Well, the question is, if the maximum speed in inertial reference frames is c, what is the minimum speed relative to it? Minimum speed happens when a particle has no movement, even subatomic particle in the structure of atoms. That is, the gravitational pressure is so high that the material becomes extremely condense and the distance between particles will go to zero.

Well, in fact I begin to understand your question a little better. And in fact, on the search for a theory of quantum gravity we need to understanding,first of all, the conflicts involving core principles of quantum mechanics, as for instance, the principle of superposition, and core principles of GR, as for instance the equivalence principle, and so on. Up to now, despite having some researchers working on topics like these, there is not any more definitive answer. But I speak of the basics. Your question goes beyond these basics.

Dear Cesar

Thank you for your honest comment. I am looking forward a new approach.

Cosmological models refer to classical spacetime-they don't have anything to do with quantum properties of gravity. There"s no such notion as a ``minimum speed'' for a particle and velocity, in curved spacetime, depends on the path.

While (hitherto) unknown properties of quantum gravity are required to derive the inflaton potential, when the description of the inflaton as a quantum field is relevant, gravity is classical.

And, for the moment, the cosmological data are sensitive to classical properties of gravity and quantum properties of matter-and are in good agreement with theory.

Dear Stam

I disagree with you. Classical cosmological models cannot describe vacuum energy.

"All our theories today seem to imply that the universe should contain a tremendous concentration of energy, even in the emptiest regions of space. The gravitational effects of this so-called vacuum energy would have either quickly curled up the universe long ago or expanded it too much greater size. The Standard Model cannot help us understand this puzzle, called the cosmological constant problem".

Kane, G., 2003, the dawn of physics beyond the standard model, Scientific American, vol. 288(6), p.68-75.

Of course they can, by the cosmological constant; and they do, since it's sufficient.

The statement quoted is, simply, wrong. The contribution of the zero point energy of the Standard Model fields quoted was computed in flat spacetime-and the backreaction of the spacetime to it isn't known how it is to be computed, even in principle. That's why identifying the zero point energy of the Standard Model fields in flat spacetime with the cosmological constant doesn't make sense. So the statement about a tremendous concentration of energy is wrong, that's all.

This was a problem, when it was thought that the cosmological constant vanished; it's no longer an issue, now that it is known to be non-zero.

Dear Stam

When and who has done it? And what is its value?

The value of the cosmological constant (among the other parameters) has been measured-for instance by the Planck collaboration: https://www.aanda.org/articles/aa/full_html/2016/10/aa25830-15/aa25830-15.html

Cf. also the review of the work by Riess, Perlmutter and Schmidt: https://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

Dear Stam

There are many measures of cosmological constant which are not same, for example, see:

http://iopscience.iop.org/article/10.1086/303583/fulltext/35047.text.html

https://cds.cern.ch/record/485959/files/0102033.pdf

http://www.bo.infn.it/sm/papers/Antilogus2.pdf

"Exactly what the value of the cosmological constant is, though, is controversial. There are different ways to measure the cosmological constant, and physicists have known for a few years that the different measurements give different results. This tension in the data is difficult to explain, and it has so-far remained unresolved."

https://www.forbes.com/sites/startswithabang/2017/05/30/is-there-really-a-cosmological-constant-or-is-dark-energy-changing-with-time/#2c85510f78b5

What matters is whether they're compatible within a given range-and they are.

In fact the technical articles show that they are compatible. Of course it's important that new ways of measuring it be developed, in order to probe whether additional fields might contribute. But, for the moment, no additional fields seem necessary and the cosmological constant is sufficient.

Once more: it doesn't make sense to compare the cosmological constant with the zero point energy of quantum matter on a flat background. The comparison is meaningless, for the reasons mentioned in a previous message.