I’ve learned from many posts on this site that matter and bound systems don’t expand with space because the forces in bound system overcome space expansion of the universe, so i wonder how would it be in the case that space contracts.
If the universe contracts, will atoms and bound systems such as galaxies,solar system also contracts?
If the universe contracts, will atoms and bound systems such as galaxies,solar system also contracts?
Let us make a distinction between classical and quantum mechanical frames.
In classical frames, as with galaxies and clusters of galaxies, the changes in the gravitational potential will start being large when the contraction is very large. For order of magnitude numbers see the answer here .
For quantum mechanical systems, like atoms and molecules to start with, agravitational contraction will be a correction to the binding potentials, an extra fine structure to the energy levels, similar to the one that appears in external magnetic fields. If the effect becomes stronger than the binding potential collapse will happen, as in neutron stars, then leading to black holes and singularity.
First of all, about your phrase if the universe contracts. There is very little experimental evidence for this ever happening, though because we have little knowledge about the nature of dark energy the future contraction of the universe has not been ruled out. In particular, $\Lambda$CDM model (the standard model of cosmology) predicts that the universe will be expanding indefinitely. Cosmological models that do allow contraction following expansion include ekpyrotic universe, some stringy cosmologies, massive graviton theories etc.
So, unlike the questions about effects of universe expansion on bound systems, which depends among other things on current or past properties of dark energy, your question asks for speculations about properties of a poorly understood (at least in the context of its long term evolution) physical phenomenon in a possibly quite distant future.
But we can conjecture, that if, say, the contribution of dark energy in such a distant future changes sign and causes contraction, the absolute value of such contribution would be at least comparable with its value presently. And so as the universe would be contracting toward the Big Crunch (or Big Bounce), the new behavior of dark energy would remain noticeable only at the largest of scales: galactic clusters and superclusters. For galaxies and below this change would be non-detectable. Of course, once contraction brings together enough mass, ordinary gravitational interaction would be disrupting first the largest structures (galactic clusters merging) then downwards toward smaller scales.
