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I'm envisioning an analogy of the universe as a plane with marbles in that plane to represent different planets.

Now, if this plane expands how does this work? I assume that it is not like 'nothing' becomes 'something' then but rather expanding/stretching the universe; but doesn't this imply that everything around us is actually stretching/becoming bigger (like every atom/quarks) becomes a little bit bigger? Or is it just the space between those subatomic particles and combinations of these become bigger?

An example could be the structure of carbon dioxide becoming larger, but only because there is more space between the carbon and the oxygen atoms.

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It would, if there were no interactions.

However, everyday matter is held together by other kinds of forces (electromagnetic, mainly). These are quite strong, and any "stretching" of space will be counteracted by these forces "pulling" the atom/molecule/object back to its original size.

So the expansion of the universe only matters on the larger, cosmic scale, between objects like galaxies which are separated by a large enough distance that they don't affect each other too much, gravitationally speaking.

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The expansion of the universe it self does not cause atoms to increase in size (because of the electromagnetic forces holding them together), but it does cause galaxies to move apart from each other (e.g., observed galaxy redshifts and Hubble's Law).

In reality, the expansion of the universe is known to be accelerating slightly (see Perlmutter et al., 1998). This acceleration puts a very small outward force on everything (including atoms). Although the electromagnetic forces in atoms hold everything together, it causes electrons to orbit protons at an (infinitesimally) larger distance from them.

If the acceleration of the universe's expansion increased many times over, this could have the potential to tear matter apart. The case of extremely large expansion acceleration is called the 'Big Rip'.

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No - Distances between objects get larger, but galaxies and clusters are dominated locally by gravity. The scale at which the expansion of the universe is significant is larger than the largest bound structures in the universe.

If you thought objects in the universe grew and stretched with the expansion, you would be forced to predict things which we do not actually observe, like the tearing apart of galaxies/clusters of galaxies at very high redshifts.

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Ummm this question made me think about a lecture from my teacher. When he was teaching us about the Big Bang theory!

From Wikipedia: The big bang states: The Big Bang theory is the prevailing cosmological model that describes the early development of the Universe.1 According to the theory, the Big Bang occurred approximately 13.798 ± 0.037 billion years ago, which is thus considered the age of the universe. At this time, the Universe was in an extremely hot and dense state and began expanding rapidly. After the initial expansion, the Universe cooled sufficiently to allow energy to be converted into various subatomic particles, including protons, neutrons, and electrons. As stated here.

Example of balloon:

So what you can imagine, there is a baloon with some dots on it. When you are blowing it, the balloon gets bigger, its size expands. But the dots stay where they were. There do comes a change in their size too. Galaxies expand too, but that doesn't mean that there is amount being added, but that means there is some space some extra space being added to it.

Objects expand:

Objects around you aren't expanding. Because this change would occur in years, so its almost ~0 this size as the changes occur inside the atom, atom contains magnetic field by the movement of electrons that would lesser down expansion and bla bla which is Chemistry so skip this. However, galaxies, stars, and on whole universe is expanding! And its been years it was expanding, and will expand! :)

Your plane example:

And your plane? Imagine that the plane is expanding. Hey wait! try this one (if possible, as this one would explain it fairly), place some magnets over a magnetic field, make sure north faces the north so they keep floating. Now when the surface expands, the magnets would stay there! They won't move backward or forwards just as the universe (plane) is moving. Similarly, as universe expands, planets don't expand! As they are not stitched to the universe or clamped to the universe. They are free moving.

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