Not sure what constitutes "provable" but the extremely homogeneous nature of the cosmic microwave background is the best observational evidence for homogeneity.

However, this is not precisely homogeneous due to matter fluctuations on the order of one part in 10^5 but these fluctuations are random (Gaussian noise) so there is no preferred spatial pattern,

Dear Professor Bothun

Thank you for important mention. Another question; there is a constant parameter c (light speed) in the Friedmann equation that is not constant in the real space. Is not necessity to reviewing the Friedmann equation?

Dear Professor Javadi,

As far as I know there is still no clear proof the speed of light (in space) varies, are there ?

Dear Adrien

Einstein's theory of General Relativity

Suppose that you have a clock and a ruler (which is not rotating with respect to stars) and that you are not accelerating (inertial). Locally (where you are) you will always measure the speed of light at 299792.458 km/sec. However in the presence of gravity if I am at a different location than yours then I could measure the speed of light at your location to be any value smaller than or greater than 299792.458 km/sec. It depends on where I am and where you are (it depends on locations). So in the presence of gravity the speed of light becomes relative (variable depending on the reference frame of the observer). This does not mean that photons accelerate or decelerate; this is just gravity causing clocks to run slower and rulers to shrink.

http://www.speed-light.info/speed_of_light_variable.htm

Also for its analyzes see:

Reconsidering relativistic Newton's second law and its results

Also for its analyzes see:

Reconsidering relativistic Newton's second law and its results

http://gsjournal.net/Science-Journals/Essays/View/5518

The CMB provides evidence that the universe was largely homogeneous 13.5 billion year ago - at small scales it is obviously no longer homogeneous.  The critical question is whether our presumption of large scale homogeneity remains valid, since conditions can only be observed at large scales for the distant past...   Please see http://arxiv.org/abs/1109.2314.

FYI - also see http://sci.esa.int/planck/51551-simple-but-challenging-the-universe-according-to-planck/ and http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe - which states

... One of the most surprising findings is that the fluctuations in the CMB temperatures at large angular scales do not match those predicted by the standard model – their signals are not as strong as expected from the smaller scale structure revealed by Planck.

Asymmetry and cold spot

Another is an asymmetry in the average temperatures on opposite hemispheres of the sky. This runs counter to the prediction made by the standard model that the Universe should be broadly similar in any direction we look...

Dear Prof. James Dwyer

Thank you for your interesting comment. I have learned of you mentions.

Dear Hossein,

Thanks for your kind remarks - I'm glad to help, but I must disclose that I'm merely an interested lay person...

Dear Prof. James Dwyer

You are most welcome. I hope learn more of you.

Please see my new work; Reviewing Friedmann Equation and Inflation Theory by Sub Quantum Energy, link below:

http://gsjournal.net/Science-Journals/Essays/View/5534

I am looking forward your opinion.

Best Regards

Hossein

Dear Prof. Hossein Javadi,

Thanks again - I'll try to respond more directly.

Sincerely,

James

Dear Prof.  James Dwyer

Thank you for you kindly respond.

Best Regards

Hossein

Dear Hossein,

In the paper you refer to, of which I could read the abstract, you state that you are reconsidering relativistic Newton's second law. How and why do you do that? In GR it is a standard procedure to write Newton's equation in covariant form.

Dear prof. Matts

"How and why do you do that?"Thank you for your important question.

AS you know modern physics is based on relativity and quantum mechanics. But there are some unanswered questions or complex concepts in modern physics. The questions that modern physics does not have answers for, and the physicists believe that it is due to the inability of theories (1). I have studied, searched and thought long years, then I Hove found some reasons that we should reconsider relativistic Newton's second law, Idid. You can see my reasons and my work on following articles;

New Discoveries and the Necessity of Reconsidering the Perspectives on Newton's Second Law

Reconsidering relativistic Newton's second law and its results

With Best Regards

Hossein

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

http://article.sapub.org/10.5923.j.jnpp.20120203.02.html#Ref

http://gsjournal.net/Science-Journals/Essays/View/5518

Dear Hossein,

In this discussion forum we address each other by first names without titles.

I have read the first page of your paper New Discoveries and the Necessity of Reconsidering the Perspectives on Newton's Second Law. You start by referring to the withdrawn result of an experiment which was wrong due to technical problems with time.keeping.

Your equation (1) is not based on anything, you have simply invented SQE, and then you go on stating that Relation (1) shows that SQE...

Instead you should have said that you assume that Relation (1) is valid, and before going to the consequence you should have motivated your assumption by some observations or references.

I would not have accepted this paper if I had been the referee.

Dear Prof. Matts Roos

Thank you for your respond.

"Instead you should have said that you assume that Relation (1) is valid, and before going to the consequence you should have motivated your assumption by some observations or references."

You are right, I agree with you. It needs an other article that I have did before and linked in the first parageraph as [6]. Please see section 2 in paper, it is here;

2. Sub-Quantum Energy

According to the principles of modern physics, Sub-quantum energy (SQE) [6] is preferred and defined in a way that it could be generalized and by using it, explained quantum and relativistic phenomena.

Best Regards

Hossein

Dear Maxim

Thank you for interesting paper.

Let’s review the Friedmann equation which is in the heart of the standard model of cosmology. Results of Friedmann equation is depended to speed of light. [Relations (2.2), (2.3), (3.7) and (3.8) in your paper].

In special relativity the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. But in the presence of gravity the speed of light becomes relative. Contrary to special relativity, the measured speed of light in a gravitational field is not constant, but these variations depend upon the reference frame of the observer; what one observer sees as true another observer sees as false. However, the speed of light in general relativity is not constant.

In addition, in quantum field theory, the vacuum state is the quantum state with the lowest possible energy. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential as well.

[To see the steps how Einstein theorized that the measured speed of light in a gravitational field is actually not a constant but rather a variable depending upon the reference frame of the observer: Einstein wrote this paper in 1911 in German:

http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1911_35_898-908.pdf

http://www.speed-light.info/speed_of_light_variable.htm]

Anyway, for long time seemed the Friedmann equation is able to explain universe, but in recent years, the cosmological constant was of interest to cosmologists. However, these two equations are unable to explain before the Big Bang. Thus this paper, from a new approach, turns out to merge the fundamental principles of quantum physics, relativity and classical mechanics through a new definition of rest state of particles like photon, and attempts to present the reasons and the possibilities of the existence of the superluminal speeds. So according to this new view some complex concepts and unanswered questions is explained in this paper.

https://www.researchgate.net/publication/279446746_Graviton_and_cosmology_equations_before_the_Big_Bang?ev=prf_pub

https://www.researchgate.net/publication/264810425_Beyond_the_Modern_Physics_and_Cosmological_Equations?ev=prf_pub

Article Beyond the Modern Physics and Cosmological Equations

Article Graviton and cosmology equations, before the Big Bang