According to theoretical physicists, due to the Big Bang, the universe is expanding.
Stuff isn’t just expanding into available empty space: space itself is expanding.
Galaxies are rushing away from each other at a rate proportional to the Hubble Constant (you go look it up…I don’t wanna ). Logically, this also means individual objects IN those galaxies also expand away from each other at that rate.
What happens when electrons get too far from the atomic nucleus, or the quarks that make up protons and neutrons get too far from each other?
Nope. The forces which hold galaxies and everything smaller than galaxies together are stronger than whatever dark force is pushing the space between galaxies (or groups of galaxies) apart.
Someone will be along shortly to explain in big words.
OK, now I’m upset about the disappearing of old threads. There was a classic (Threadspotted, even) on this exact topic. My favorite line from it was “The Universe is full of stars. Why are there no stars in my nose?”.
I will add, though, that there are models in which the dark energy actually increases in strength with time, such that eventually, everything (including the quarks in protons and neutrons) would be pulled apart, in a cataclysmic Universe-ending event dubbed the “Big Rip”. There’s little theoretical reason to expect the dark energy to behave in this way, though the data currently slightly favor such models over the simpler constant-lambda models. The error bars are still consistent with constant-lambda, though, so Occam currently tells us that that’s more likely to be correct.
But to answer the OP more closely, the expansion of space is a very gentle and slow process. It is trivially easy for atomic particles to maintain their distances from their neighbors, because subatomic forces are so big relative to the acceleration required to maintain their neighbors. The expansion of the universe is barely significant on the scale of our Milky Way’s neighborhood. For practical purposes the only significant force on the scale of a single galaxy is gravity, and on smaller scales like our solar system the significance of the expansion is incredibly smaller still.
Due to the Hubble constant making the galaxies expand away from us…the farther away, the faster they recede…thus an event horizon of sorts denotes the edge of the observable universe; the edge being a distance where the receding galaxies are going at the relative speed of light.
If current models of the universe are correct…that the rate of universal expansion is speeding up…then the lightspeed horizon becomes closer.
Actually it’s the other way around.
Recall Hubble’s law states v=Hd, which just means that if Galaxy B is twice as far from us as Galaxy A, then Galaxy B would be receding from us twice as fast as Galaxy A. It would stand to reason that the distance d=c/H – the Hubble Distance – where galaxies are receding from us at the speed of light, would form an event horizon from beyond which light could not reach us. Except that the Hubble constant is not really constant; in actuality it decreases over time, and the Hubble distance increases in inverse proportion, so that the edge of the observable universe is always slowly creeping outward. Which leads to the interesting situation of being able to observe some objects at the edge of the universe receding away from us faster than the speed of light.
Besides, the real limit in forming an edge to the observable universe is that the universe isn’t old enough for things to be further away and their light to have had time to reach us. We can see the cosmic microwave background as it is - this is the glow the universe had when atoms first formed (and of course long before galaxies did).