When dealing with infinite space of the universe, most of us could get confuses easily.

The curved surface of the Earth can be used as an analogy. The Earth's surface is finite in area, but unbounded (no boundary). A traveller will not meet any edge or boundary in whatever direction he goes.

Similarly space could be finite in volume, but without any edge or boundary. An astronaut could, in principle, pointing his rocket in one direction and would return to his starting point at the end.

The big bang theory suggests that all matters (planets, asteroids, galaxies) are moving apart from each others a.k.a expending universe.

While the matters are moving away from each others, so DOES the SPACES within them are expending (imagine the spaces are stretch in an expending universe). The matters is NOT expending in spaces that already there, but the SPACES are being stretch further when the matters expend.

Many of us often assume that universe space is infinite and the planets are moving away and filling up more spaces which is already there (like a boy moving two balls apart in a big room (where spaces already be there) which is NOT TRUE.

Universe is a hypersphere with finite volume without boundary. The volume (x, y,z, t) continues to expend (and one day may retract) as a result of the big bang explosion.

If you are interested to understand this more, please refer to Einstein's hyperspherical cosmos modeling.

Cheers.

Agreed with the forumers here.

Cosmology and theoretical sciences are started from the imagination plus some observation, measurement made. From there hypothesis were then postulated.

The beauty of sciences is it encourages questions, doubts and dare to be challenged. Nobody owns it, not even Einstein. Should someone discovers a better way of explaining the universe later, it would be rejoiced as we are one step closer to the truth.

Just to add, the reason why hypersphere is a better model:

1) It resolves the issues with hitting with a "wall" at the end of the spaces

2) It complements with General Relativity of space and time curvatures

3) It agrees with big bang discovery (In mid-1965, two pyhsicists in Bell Telephone Company discovered some mysterious radiation (white noise) from space. They revealed that it is a relic of the primeval heat, the last fading glow of the fiery birth of the universe. This discovery provides a solid evidence of a singularity explosion leading to the expension of the universe.

4) It overcomes the limitation Of Steady State theory (Hermann Bondi, Thomas Gold and Fred Hoyle)
- The universe is infinite in age (no start, no end, always there). To overcome the thermodynamics heat death, low entropy matters are postulated to be contineouly created within the universe.
- Unfortunately the discovery of cosmic background heat radiation in 1965 has nailed this postulate down into the coffin.

Although Steady State theory has been replaced, it remains an important idea that:

A) It demonstrates the logical possibility of a universe without creation nor creator is possible
B) An universe which will not heat death after infinite time has passed is also possible
C) All processes, the matters could be attributed to the natural mechanisms

Feel free to share your idea.

Cheers.

According to Einstein cosmos, universe is a hypersphere with finite volume without boundary.

Volumes mean matters, spaces and time. Due to the expansion, the matters are moving away from each others and the spaces between them are stretched, hence the volumes of the hypersphere is larger but still finite. Imagine a tennis ball (the hypersphere universe) expands become a basketball.

A finite (finite doesn't mean fix, it means contain) volumes can expand, this is the whole idea.

Just ask another question, can an infinite volumes expand further. This question is meaningless as infinite volumes mark the highest volumes imaginable. Just like what you have quoted.

Ever heard of Doppler Effect? Imagine your are driving a car and an ambulance (with siren on) from the opposite direction. The sound signal from the siren would be weak, stronger, strongest, weaker, weak as the ambulance is moving closer to you and then moving away.

Now replace your car with planet earth and the ambulance with a planet under observation, and sound to be replaced by light.

Distance from two planet could be estimated using the method. Cosmologists encountered that the distances between the planets are getting further, hence by looking backward, these planets were closer and at a point, there were together (singularity) before the explosion.

Don't have answer to your question though, on measuring the perimeter of the universe. However, aren't the extension of the distance between two planets signify the universe expansion already?

Cheers.