Can “big rip” rip apart an atomic nucleus?

Question

Some scenarios describing the fate of the matter vs dark energy tug of war on the universe involve the acceleration of the universe increasing to the point that it ends up ripping apart even atoms. This is called the Big Rip.

This makes no sense to me. It looks like all of these GR models of the universe assume it has a uniform isotropic distribution of matter and energy. This works great at long scales, but is also clearly wrong even at the length scale of the separation of galaxies.

The density of atomic nuclei remains the same even though the universe is expanding even as we speak. I don't think the "scale" in the Friedmann equation can be interpretted so literally. Or maybe said better, it's got to break down when the cosmological horizon distance gets to the scale where the isotropic assumption breaks down, right?

How can scientists be claiming that run away expansion will rip apart atoms?

Answer 1

Look at this paper:

"In an expanding universe, what doesn't expand?" by Richard Price

The expansion of the universe is often viewed as a uniform stretching of space that would affect compact objects, atoms and stars, as well as the separation of galaxies. One usually hears that bound systems do not take part in the general expansion, but a much more subtle question is whether bound systems expand partially. In this paper, a very definitive answer is given for a very simple system: a classical "atom" bound by electrical attraction. With a mathemical description appropriate for undergraduate physics majors, we show that this bound system either completely follows the cosmological expansion, or -- after initial transients -- completely ignores it. This "all or nothing" behavior can be understood with techniques of junior-level mechanics. Lastly, the simple description is shown to be a justifiable approximation of the relativistically correct formulation of the problem.

Short summary
All or nothing behavior: If the binding force is greater, the object does not expand significantly. If the cosmological costant is stronger, the object expands.

Hence, as the cosmological constant grows to infinity (or minus infinity, according to the usual convention), more and more strongly bound systems are ripped apart.

However, this analysis assumes the binding force (i.e. gravity or electrodynamics) decreases with distance.

The strong force, however, increases with distance.
So the cosmological constant versus the strong force is still an interesting question.

Answer 2

I looked at the link, and it is a general scenaria link, so I will concentrate on the isotropic part of your question.

You say:

The density of atomic nuclei remains the same even though the universe is expanding even as we speak.

Define density of a piece of metal. It is the number of atoms*(atomic mass) per cubic centimeter. Number is constant. Consider atomic mass constant too. Cubic centimeter was defined as a cm cubed, drawn on a piece of metal at some central bank. Now they take the wavelength of some atom.

The universe is expanding, from the time of big bang, at each point of space. It means as an example that the distance between these two points : is expanding at the rate of expansion of the universe , and the dots are expanding, and this page is expanding and ... The same is true for matter composed of atoms.

We would not notice the expansion, even if our senses were sensitive enough to be able to see such small cosmological changes, because of our definition of distance and units in general.

So the isotropy and uniformity do not have a role to play in an argument whether the big Rip, as expounded in the link you gave, can happen or not.

Some theory has to enter, see for example the link provided by Jim Graber above, where results are conditional to the strength of forces.