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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 general relativity (GR) models of the universe assume it has a uniform isotropic distribution of matter and energy. This works great at long scales, but it 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 interpreted 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 runaway expansion will rip apart atoms?

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    $\begingroup$ I think you would have to ask the Big Rip proponents because no one else believes that those scenarios are compatible with the physics we know. I have asked similar questions to the Big Rip champions and the answers never made any sense, either. So I can only say that I totally share your sentiments. $\endgroup$ Commented Apr 9, 2011 at 5:16

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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.

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    $\begingroup$ +1, this is the correct picture. Cosmological constant (or rather expansion due to it) is negligible for microscopic scales but if it somehow manages to diverge to infinity it will naturally become relevant even at these scales and one needs to compare binding forces with this tearing due to expansion. $\endgroup$
    – Marek
    Commented Apr 9, 2011 at 13:11
  • $\begingroup$ So to summarise this conclusion in terms of the actual question:(1) The Big Rip will happen (up to atom scale at least);(2) Cosmological isotropy assumptions dont make any difference - the basic theory is sound;(3) Nuclear Rip may or may not happen. Is this the "correct picture"? $\endgroup$ Commented Apr 12, 2011 at 18:42
  • $\begingroup$ @Roy Simpson: The big rip will probably not happen -- unless dark energy has the right equation of state to make it happen. $\endgroup$
    – user4552
    Commented Aug 5, 2011 at 4:01
  • $\begingroup$ The paper is interesting, but it's completely classical. It's not at all obvious to me that the classical approximation is valid. A classical "atom" can have any size. A quantum-mechanical atom has a size that is fixed by fundamental constants, and likewise for a nucleus. Their definition of the "physical" distance r as a "proper distance" also seems weak to me. I don't see the justification for assuming that such a definition makes sense. The reason we are normally justified in talking about rulers, etc., is that the length of a ruler is defined by the sizes of atoms. $\endgroup$
    – user4552
    Commented Aug 5, 2011 at 4:18
  • $\begingroup$ This answer is wrong and I don't understand why it was accepted. The cited paper assumes perfect homogeneity (down to the atomic level!), while the question was explicitly about the effect of inhomogeneity. And even in a perfectly homogeneous universe the claim in the abstract is wrong in general, unless you interpret it tautologically as "systems either expand without bound or don't". Looking at the paper, it appears he only considered some specific functions $a(t)$ where the conclusion happens to hold. It doesn't hold in big rip cosmologies. $\endgroup$
    – benrg
    Commented May 7, 2023 at 21:56
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The answer from 2011 is wrong and I don't understand why it was accepted. The question is about the effect of inhomogeneity on a big rip, but the paper cited in the answer assumes perfect homogeneity, so it's irrelevant to the question.

(The paper is also irrelevant to real life, since perfect homogeneity at the atomic level is inconsistent with the existence of atoms. This is a strangely common mistake and I've written several answers about it, including this one. On top of that, even if you do assume perfect homogeneity, the claim in the abstract is still not correct, unless you interpret it tautologically as "systems either expand without bound or don't". Looking at the paper, it appears he only considered some specific functions $a(t)$ for which the conclusion happens to hold. It doesn't hold in general, and it doesn't hold for big rip cosmologies in particular.)

As Luboš Motl said in a comment, there doesn't seem to be any plausible sort of stuff that would lead to a big rip, but if you imagine that something with the necessary properties exists, you can perhaps get an idea of how it might behave in an inhomogeneous world.

In standard cosmology, dark energy is perfectly homogeneous down to subatomic scales. The expansion of the universe is just the relative motion of galaxy clusters, and doesn't push atoms apart, but dark energy does push atoms apart, because it's everywhere. Since it's the same everywhere, it just exerts a small constant outward pressure, so atoms are slightly larger than they would be if $Λ=0$, but don't grow over time.

In slow-roll inflation, the inflaton field is somewhat like dark energy, except it's not constant over time; if it were, there would be no way to coordinate an orderly exit from inflation on a large/infinite spacelike surface. Instead, it has a value that is set by the event that triggers inflation, evolves over time (the slow roll), and triggers the exit when it reaches a certain value. In other words, this all-space-permeating substance has a built-in clock, and in principle you can read the clock by local measurements to determine what phase of inflation you're in.

The quintessence that caused a big rip would be similar to that. Spacetime would be filled with ticking time bombs, and in principle you could read the nearest one's clock face by local experiments. They would be affected by gravity, since everything is. They would be lensed by clumps of matter, and would collide with a result determined by some unknown dynamics. But it's not terribly farfetched to suppose that this wouldn't stop the countdown to doomsday. It just means that the final singularity would not be a nice flat hyperplane, but would have a more complicated shape—as is also the case for a more realistic treatment of the big crunch, taking inhomogeneity into account. In the last few yoctoseconds before the end (according to the nearby clocks), nuclei would be "ripped apart" in the sense that their diameter would go to infinity, though they wouldn't really have time to notice.

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