This sparked to mind in a different thread and was on its way to going off topic so I decided to make a topic of its own.
This thread is to discuss the possibility of an infinite universe, how to validate if it is true or false, and some of the consequences and thought experiments that go along with it being true or false.
What occurred to me is that the universe could be much larger than the CMB suggests. It is logical to say that "IF" the universe had a beginning (under evolutionary conditions) then that will be the furthest point away that we could observe. However, this does not exclude the possibility that what we observe at the CMB distance continues on forever.
On the other hand, if the universe did not have a beginning stage then it would be likely we would be capable to observe beyond a CMB distance of which may contain familiar things like stars and galaxies.
I lean towards it having a beginning due to the nature of the CMB observations and other supporting scientific data. So with that said, it is possible that the universe could be infinite in size, however, the furtherst point at which we can currently see is precisely the age of the universe known to be as you said around 13.7billions years.
Now in a thought experiment we could logically create the scenario where there are observers separated by twice the distance of the CMB, so 27 billion light years. When we draw this out we could draw 10 dots representing 10 observers, and separate each dot equally with it's neighbouring dots, a distance that represents 27 billion light years.
Next we could draw a circle around each dot that represents the visualized CMB for each observer, a circle with a 13.7 billion light year radius. Each circle would represent the maximum detectable size of the universe for each observer in its center. In this case we would have an apparent 10 universes according to the 10 individual observers. Each observer independently measures nearly exactly the same distance for the CMB, a value of 13.7 billion light years from their position.
However, what they all share in common is that they all reside in a singular and unified universe of suggestible infinite size that burst into a beginning at precisely the same moment across thousands of billions of light years. And theoretically speaking thousands of billions and beyond and beyond.
To test if the above is true I believe all that would need to be done would be the following.
We would only need to observe the CMB and determine whether it is changing at a rate faster than would be acceptable by the laws of physics. For example, are the shapes and/or patterns of the CMB moving or changing at velocities that exceed the speed of light etc.
The reason why this would be possible to have it change faster than the laws of physics without breaking the laws of physics would be due to an expanding view of the cosmos as further points of the first events (the beginning) reach us. Thus giving us an ever expanding view of the universe, not only that, but also an accelerating growth in size due to the exponentially growing circumference of the CMB.
To elaborate on this. Consider that the circumference of a circle is equal to Pi x Raidus x 2
Thus doubling the radius increases the circumference 2? times.
So as time ticks on further and further Microwave background radiation reaches us, giving us the view of a larger and larger circumference that is reaching a constant in all forms observer at the center.
Theoretically speaking a relatively simple formula could be made to test this very concept.
The formula would attempt to calculate the value of energy when taking in the consideration of an ever growing circumference as the source, with the speed of light as the rate at which the radius grows, but at the same time using a constant angle for the line of sight.
Such that more and more energy funnels towards the observer as it comes from a further source. and yet taking in consideration the every decreasing strength of electromagnetic radiation over the distance.
According to the possibility I mentioned above about having an infinite potential for the size of the universe, these calculations should give some approximations of how fast the universe is growing and also allow us to predict the changing CMB radiation level of energy. (assuming my math is correct)
 (\pi) (r))
 (\pi) (r^2))
 (t))
cir : circumference m
Sa : Surface Area Sphere m
r : radius meters
c : speed of light 
t : time seconds
In one year the radius of the universe would grow:
 (3.1536x10^7seconds))
Which would be a circumference of:
Surface Area:
What this predicts (under the case of an infinite potential universe) is that the CMB would be viewed to grow greater and greater in density and energy intensity. As time passes on, a greater and greater volume of material per unit area view would be exposed as the observable and detectable universe grows at the speed of light in all directions, which is equivalent to say the growth of time. And as such this would be true for any observer in any position they find themselves in the universe.
What is great is if this is proved incorrect, it should suggest that the universe is not of infinite potential but is of a limited nature not only in detectability but in the literal sense of the maximum reaches of both space and time.
A further prediction would be that at some point an observer would receive energy from the big bang at such a high concentration that it could be considered to reach infinite.
This would be true at infinite points in the infinite universe and to happen at exactly the same time.
As time passes on, and as the ever further energy coming from the ever growing quantity, reaches the observer (assuming something stronger than microwaves reach the observer) to the point of which so much energy is reaching this conscious "point of time" (an observer) that the energy breaks apart all the matter down to its basics thought to be found at the stages of the big bang, and thus it all begins again.
