Is the energy density of vacuum uniform in the whole universe? This is not a duplicate. I am not asking why the energy density of quantum vacuum stays constant while the universe expands. My question is about how we know/measure that this vacuum energy density is uniform, throughout the whole universe, that is, how we experimentally know that it has the same value between the galaxies of our cluster and in the viods of space of between superclusters.
I have read this question:
Energy/mass of Quantum Vacuum
where G. Smith says:


According to the current and successful Lambda-CDM model of cosmology (which has a level of acceptance among cosmologists similar to that of the Standard Model among particle physicists), the energy density of the vacuum is $5.4\times 10^{-10}\,\text{J/m}^3$ and remains constant as the universe expands.Its numerical value is determined by fitting the Lambda-CDM model to precise observations of the cosmic microwave background.


Now this means that this is the energy density of vacuum. 


The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10^−9 joules (10^−2 ergs) per cubic meter.
    Vacuum energy is an underlying background energy that exists in space throughout the entire Universe.


https://en.wikipedia.org/wiki/Vacuum_energy
So this value is for quantum vacuum.


In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. 


https://en.wikipedia.org/wiki/Vacuum_state
What is not explained is, how we experimentally measure this value so, that it is the same constant for the whole universe. Now space is expanding uniformly on the large scale in the universe.
I do understand that, but there are areas of the universe, where dark energy is more dominant, and there are areas where gravity is more dominant. What is not explained is, how do we experimentally measure the vacuum energy density in far away intergalactic viods of space (where dark energy is more dominant). Inbetween galaxy clusters dark energy is still dominant, so space is still expanding, but the expansion is only uniform on the large scale. There are regions of space where space expands faster (gravity is less dominant).
Question:


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*How do we experimentally measure that the vacuum energy density is uniform throughout the whole universe?

 A: The simple answer is that we don't know that dark energy is uniform on any but the largest scales. The only evidence we have for the existence of dark energy comes from:


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*the Sn1a supernovae light curves

*the measurements of the cosmic microwave background
Both of these measure on scales far larger than galaxies. The resolution is more like 100 to 1000 million light years than the size of a galaxy. In any case it would be hard to measure the effects of dark energy in anything smaller than galaxy clusters since these are gravitationally bound and the effect of dark energy would not be easily measurable. I confess I'm unsure to what extent the effects could be seen on the supercluster scale.
A: As far as I know (not an expert), the constant energy density you are referring to is the "dark energy" and its density is inferred from cosmological observations and inserted into Einstein equations as a constant parameter. That is, it is not measured directly but is "fixed" by assumption to be constant such that expansion of the universe will be consistent with observation. 
The second point is that, although one of the most accepted candidates for dark energy is the vacuum zero point energy, even theoretically it does not work out very well in terms of numbers. I don't think we have any measurements on that even from the lab, let alone distant galaxies. 
Bottom line, we don't know much about it and the best we can do is assume a constant uniform energy to balance out our equations to be consistent with observation. 
A: 
Is the energy density of vacuum uniform in the whole universe?

No. It varies in a gravitational field. That's why Einstein said “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”.

...how do we know/measure that this vacuum energy density is uniform, throughout the whole universe, that is, how we experimentally know that it has the same value between the galaxies of our cluster and in the voids of space of between superclusters.

We look at galactic redshift and the motion of galaxies. If galaxies aren't moving apart in one region due to gravity, but they are in another region, I think that's the evidence that the vacuum energy density isn't uniform across the two regions. Also see papers like interacting and inhomgeneous vacuum energy by Josue De-Santiago, David Wands, and Yuting Wang.   

I have read this question: Energy/mass of Quantum Vacuum where G. Smith says According to the current and successful Lambda-CDM model of cosmology (which has a level of acceptance among cosmologists similar to that of the Standard Model among particle physicists), the energy density of the vacuum is $5.4\times 10^{-10}\,\text{J/m}^3$ and remains constant as the universe expands. Its numerical value is determined by fitting the Lambda-CDM model to precise observations of the cosmic microwave background.

Just because some idea has a lot of acceptance among cosmologists doesn't mean it's correct. In all situations I know about, conservation of energy applies. I know of no actual situation where it doesn't. So I'm wary of a hypothesis that says energy is created ex nihilo.  

Now this means that this is the energy density of vacuum. 

The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum. The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behaviour of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10^−9 joules (10^−2 ergs) per cubic meter.


Like Michael Walsby said in his comment, there's a discrepancy of 40 orders of magnitude between the QM vacuum energy density and cosmological observations. And as Svend Rugh and Henrik Zinkernagel pointed out in their 2002 paper on the quantum vacuum and the cosmological constant problem, photons do not scatter on the vacuum fluctuations of QED. If they did, “astronomy based on the observation of electromagnetic light from distant astrophysical objects would be impossible”. Hence when they say the QED vacuum energy concept “might be an artefact of the formalism with no physical existence independent of material systems”, I think they’re right. However, I also think this is correct: 

Vacuum energy is an underlying background energy that exists in space throughout the entire Universe.

There is energy in space. And like I said, it varies in a gravitational field. But I would also say the energy of the gravitational field doesn’t consist of quantum fluctuations, and nor does dark energy. Schrodinger talked of "cosmic pressure". See Alex Harvey's How Einstein Discovered Dark Energy where Schrodinger's 1918 paper is translated into English. 


In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. 


I'd say cosmology refers to relativity more than QFT, and the vacuum catastrophe along with Rugh and Henrik means there's an issue with the QED vacuum energy concept. So I'd set it aside if I were you.    

What is not explained is, how we experimentally measure this value so, that it is the same constant for the whole universe. Now space is expanding uniformly on the large scale in the universe.

When we measure galactic redshift on the largest scale, we're measuring the effect of the vacuum energy or "cosmic pressure".  

I do understand that, but there are areas of the universe, where dark energy is more dominant, and there are areas where gravity is more dominant. What is not explained is, how do we experimentally measure the vacuum energy density in far away intergalactic voids of space (where dark energy is more dominant). In between galaxy clusters dark energy is still dominant, so space is still expanding, but the expansion is only uniform on the large scale. There are regions of space where space expands faster (gravity is less dominant).

OK fair enough.  

How do we experimentally measure that the vacuum energy density is uniform throughout the whole universe?

You look at the galactic redshift on the largest scale, and see if fits with the Hubble parameter everywhere. Allowing for time dependence. 
