Many physicists believe our universe is undergoing a radial spatial expansion based on a discovery made by Edwin Hubble that distant galaxies are moving away from us. They also believe the universe began with a “Big Bang” because if one traces the motion of these galaxies back in time they merge at point in the past.
Alexander Friedmann developed the theoretical foundations for this expansion when he realized a solution to Einstein’s field equations describes a spherical universe, which starts from a point (called a singularity) whose radius expands with time to become the universe, as we know it today.
This observation, that the universe is expanding and Friedmann’s solutions provide the foundation for the Big Bang Theory and the Standard Model of cosmology and particle physics, which for the past 25 years has given us a complete mathematical description of the particles and forces that shape our world. It predicts with such accuracy the observable microscopic properties of particles and the macroscopic cosmologic properties stars and galaxies that many physicists believe it is the ultimate theory of mass and energy.
One can understand how an expansion of universe could explain the observations made by Hubble by using an analogy of an ant living on a surface of a balloon. First, one must imagine that the ant can only move on the surface of a huge balloon, which to the ant’s understanding is the total extent of universe. At an early stage of the balloon-universe, the ant measures distances between separate points on the balloon, which serves as his standard. As the balloon is inflated, the distance between the same points is measured and determined to be larger by a proportional factor. The surface of the balloon still appears flat, and yet all the points have appeared to recede from the ant, indeed every point on the surface of the balloon is proportionally farther from the ant than it was earlier.
Similarly, galaxies in our universe would appear to recede from us as if the universe was expanding for the same reason that the points on the balloon receded from the ant as his or her universe expands.
As mentioned earlier the Standard Model successfully answers many of the questions regarding the cosmological structure of the universe and the creation of subatomic particles based on the existence of an expanding universe.
However, for all of it successes it has one very obvious shortfall in that it does not answer the question “What is the universe expanding into and how do the physically properties of the dimensions interact to generate the particles and forces in our world?”
But there are some who say that it would not make any sense to ask what our universe is physically expanding towards for the same reason that it would not make any sense for the ant in the earlier example to ask what his “universe” is expanding towards. This is because the ant is confined to the two-dimensional surface of the balloon; the existence of a universe outside of that surface would not affect him.
This would be true if physicists and cosmologists had not used the concepts of the dimensional interactions they associate with a physically expanding universe to develop the abstract mathematical basis for Standard Model of cosmology and particle physics. Therefore, their existence, according to the assumptions on which the Standard Model is based must have a physical along with an abstract effect on our universe.
However, even though we are confined to our three-dimensional universe we can get an understanding of some of the properties of the dimension it is expanding towards by observing the effects of this expansion on our universe.
For example, we know that three-dimensional space is must be expanding towards a higher spatial dimension not a time or space-time dimension because the observations made by Hubble indicate the universe is undergoing a spatial expansion.
Presently, we understand very little about the physical properties of these higher spatial dimensions due, in part to the fact many scientists seem to be satisfied with defining them in only in terms of their abstract mathematical properties instead of attempting to understand them in terms of how and why their physical interactions with three-dimensional space can explain and predict the forces that shape our world.
However, history has shown us that the greatest advancements in civilizations have been the result of looking beyond what we can see and physically “boldly go where no one has gone before.”
Later Jeff
The “Shadows” of four spatial dimensions
Copyright 2008 Jeffrey O’Callaghan

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going where we are not,because we left it behind us.
It sounds interesting but I am not sure that I agree with you completely….