Do the cosmological expansion affect binding systems

[dimilion]

It is known that in result of the cosmological expansion the distances between galaxies increase according Hubble law v=H*r. Distant SNeIa show that the dark energy accelerates the expansion. I heard in a scientific popular transmission that in result of the acceleration of expansion, every molecule, atom and even nucleus will dissipate.
I think that the binding object like planetary systems, atoms, nuclei etc. not expand. What is the true?

 

[Chalnoth]

Well, there is some effect, but it's not quite what you're probably thinking.

First of all, no, the expansion itself has no effect whatsoever on the dynamics of bound systems. You can understand the properties of a bound system in an expanding universe without paying any attention at all to what the rest of the universe is doing.

That said, dark energy does have an effect on the stability of bound systems, though the effect is very small for most any system you might think of, just because the density of dark energy is so low.

If the dark energy is a cosmological constant its energy density will stay constant in time, and its effects today will, therefore, be the same as its effects trillions of years from now. However, because the dark energy induces a repulsive gravitational force, it causes systems to become unstable on large time scales. I don't think it'll have any effect on our solar system or galaxies, but it does have a limited effect on galaxy clusters and larger structures, which can be seen in the CMB as what is known as the Integrated Sachs-Wolfe effect.

But what if dark energy is not a cosmological constant. One very exotic possibility is that it is a type of matter that has a more negative pressure than a cosmological constant. This would mean that the energy density of the cosmological constant increases with time. While most theorists are extremely skeptical that such a thing is even possible, it is easy enough to imagine what might happen if such a thing did exist: its effects would be very much like that of a cosmological constant, but with the radius at which its effects become important continually shrinking.

So, if dark energy was made up of this very exotic stuff, it would mean that even though right now basically only galaxy clusters and larger are large enough to be effected by any noticeable amount, eventually that size will shrink, and its effects on galaxies will become apparent, eventually being blown apart by the repulsive force of this stuff. As the energy density continues to grow, smaller and smaller structures would be blown apart by the repulsive force. It would even become so strong that it wouldn't just blow apart gravitational systems, but also electromagnetic ones like atoms, and even nuclear bound systems like atomic nuclei. This would be our universe ending in a "big rip".

The difficulty, however, is that this violates some energy conditions in General Relativity, something that most theorists find rather unlikely. For a while physicists didn't even bother considering the possibility that we might measure the pressure of dark energy to be more negative than a cosmological constant, a position that was reversed only when it was discovered that if dark energy and dark matter interact, we might get something that looked like it had more negative pressure than a cosmological constant, but only because we didn't take into account the interaction between dark matter and dark energy. Most still think a big rip is pretty unlikely.

 

[dimilion]

Thank you very much for the comprehensive answer of my question. Most probably, the authors of the above mentioned transmission have talked about “big rip” in case of this exotic form of dark energy.