Sorry to say, but your theory is neither scientific nor even pseudo-scientific. I would suggest you to first read some standard books on cosmology and also on relativity. Neither your knowledge about cosmic expansion, nor the framework in which relativity is valid, is correct. See some links

http://phys.org/news/2015-10-galaxies-faster.html

http://phys.org/news/2015-02-space-faster.html

http://phys.org/news/2015-02-fast-universe.html

http://curious.astro.cornell.edu/about-us/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/616-is-the-universe-expanding-faster-than-the-speed-of-light-intermediate

So, the notion of "Maitra Horizon" is not correct. Also, FYI, Einstein never called his equations Einstein field equations; and Feynman never called it Feynman's path integral approach. See point 25, in this link. http://math.ucr.edu/home/baez/crackpot.html

You can't use special relativity for cosmology, you need to study the Friedmann Equations as a minimum and preferably the FLRW metric.

Even using SR, you have a basic error when you say "Now, since this relative velocity contributed by both galaxies( each may have velocity C/2)". Velocities don't add linearly in SR, see the attached link.

https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity

Sorry to say, but your theory is neither scientific nor even pseudo-scientific. I would suggest you to first read some standard books on cosmology and also on relativity. Neither your knowledge about cosmic expansion, nor the framework in which relativity is valid, is correct. See some links

http://phys.org/news/2015-10-galaxies-faster.html

http://phys.org/news/2015-02-space-faster.html

http://phys.org/news/2015-02-fast-universe.html

http://curious.astro.cornell.edu/about-us/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/616-is-the-universe-expanding-faster-than-the-speed-of-light-intermediate

So, the notion of "Maitra Horizon" is not correct. Also, FYI, Einstein never called his equations Einstein field equations; and Feynman never called it Feynman's path integral approach. See point 25, in this link. http://math.ucr.edu/home/baez/crackpot.html

If you do not take into account the observation of the evolution of a variety of structural elements in the observable universe your assumption might make sense. In turn, this leads to some assumptions about the external space of the Universe, they will have a lot of uncertainty and contradictions. Your assumptions are based primarily on the Euclidean geometry also imply a minimum of outer space in which the Universe must expand.

What do you mean intuitively as an infinitely dense surrounding object must be the matter of our Universe. However, the classical concepts of massiveness and volume do not apply to it in the literal sense. Spacetime is an integral part of the interior of this holistic object. It makes no sense to talk about the space in the classical view, and try to place the object in it. This category is only a reality contained within the object.

What really makes sense in your considerations - this is how the top speed of propagation of disturbances forming an event horizon for the coherent structure of the Universe.

Based on the universality I can even suggest that the interaction of the dynamic system (which is our Universe) with external system should lead to the fact that you imagine infinitely thin object should have a variety of "surface" inside and outside the ratio of which must be related to some power law.

It is the task of the topology and theory which must describe the interaction of dynamical systems in the Multiverse. The "surface" difference is probably also one of the reasons for observing the accelerating expansion of the observable universe.

I would recommend you familiarize yourself with the hyperbolic geometry and dissipative system (in addition to FLRW) and want to note that the representation of FLRW and LCDM are developed at a time when the matter is considered primarily as autonomous objects in space. Then you will get the field for further reflection.

Unfortunately, the question statements and extension docx induce that crackpot index is way too high. Not following.

However any idea that does not sound like "something there is not correct since I can not imagine that such happened in reality" is probably not the original but at least constructive.

Try to look from the inside a black hole? Why not? Here is good seed to discussion. Such ideas always give ground for the imagination, although in this case we are talking about a simple analogy with a shock wave from an object moving at supersonic speed.

If one had to be unfollow from each thread where the anyone interfere with endless proofs of inconsistency of relativity theory one would have to miss some of the most actual and problematic discussions. Since the "crackpot index" there sometimes is much higher and combined with personal accusations and senseless emotions (:

Long time ago we (the people), and our Earth as well, were at the center of Universe.  Today we know, it's not true.  So, what is the meaning of "r" in your theory??

Let it be anywhere . Evenif the Universe is not symmetric , argument holds, as we are talking about only the relative velocities.

In short, no.

Not every increase in distance is actually a speed. Things are limited to moving through space at less than about 300 000 km per second. However, the thing you calculate using Hubble's law is the rate at which space appears between us and distant objects. While this is often referred to as a speed, it strictly speaking isn't, and it's not constrained in the way actual speeds are. So things at a certain distance will increase their distance from us at a rate equal to the speed of light, and things outside of that distance will do so exceeding the speed of light, and nothing especially interesting happens at the boundary.

The boundary is still interesting, since we cannot see things outside of it. It's usually referred to as the Hubble Sphere (or Hubble radius, Hubble horizon, etc) and you can read more about it in the attached link.

ps: As Marek Gutowski hints in his reply, Hubble's law can be applied to any particular point in the universe, so you could as well take a point very far away as the center defining r, and applying your argument you would have to conclude that we should be collapsed into a black hole, which evidently isn't the case.

https://en.wikipedia.org/wiki/Hubble_volume

If their length collapses to zero , they shall not cover any distance even at light speed

I'm sorry, but there are two things wrong with this claim.

First of all, a thing moving at light speed moves at light speed. That means that it will cover a distance of 300 000 km every second. The length contraction does nothing to affect that.

Second, the formula for length contraction isn't relevant in any case. Things at the Hubble horizon don't travel through space at the speed of light, which is what you'd need for them to be length contracted. Space is expanding, causing the distance between them and us to increase by 300 000 km per second.

Excellent summary Alvin, however one part isn't quite right:

AG: things at a certain distance will increase their distance from us at a rate equal to the speed of light, and things outside of that distance will do so exceeding the speed of light, and nothing especially interesting happens at the boundary.

That's correct but:

AG: The boundary is still interesting, since we cannot see things outside of it.

That is not correct. From the link (last sentence of the introduction):

Wikipedia: "the term is also frequently (but mistakenly) used as a synonym for the observable universe; the latter is larger than the Hubble volume."

We can and do see objects which were expanding away from us at a rate higher than the speed of light at the time of emission and ever since. For example, the most distant spectroscopically confirmed galaxy found to date is GN-z11, it was moving away at 2.24c when the light we see now was emitted, and it is now receding at 4.32c.

This just emphasises why trying to use special relativity is inappropriate.

My bad, thanks!

I'm a bit annoyed with myself now, since I now remember reading a list of common misconceptions that specifically mentioned the claim I made. :-/

According to physicist O. Davtyan the Universe is surrounded by geon crown with fundamental (Plank) thickness of 5.7 ·10 exp-33 cm and density of 10 exp(92)/cc. The so-called relict radiation is a part of background radiation from the geon crown.             The sources: O.K. Davtyan “Theory of Gravitational-Inertial Field of Universe”, Annalen der Physik, vol.490, issue 2, 1978, pp. 116-121; O.K. Davtyan “Fundamental Field Theory”, 2011, Yerevan, “LIMUSH“ Printhouse (available at Amazon).