Q & A: atoms in the big rip

This is about the "Big Rip" scenario. This site ( http://hubblesite.org/hubble_discoveries/dark_energy/de-fate_of_the_universe.php ) claims if there is enough dark energy, the universe will eventually acceleratingly expand to the point that even *atoms* are torn apart! The 'big rip' Wikipedia article claims likewise. Having read a little about GR, that sounds wrong to me. The expansion of the universe equations assume uniform isotropic densities. This is true at large distances and allows modelling of the universe, but it is clearly not true even at the level of galaxy interspacing. It seems the "big rip" assumes that during expansion normal matter is spreading and diluting such that eventually the dark energy is more 'dense' than 'ordinary matter' everywhere and 'wins'. However, at scales where the matter is clumped (like the galaxy or as an extreme example, the earth) the galaxy isn't diluted by universe expansion. The density of atomic nuclei aren't diluted by universe expansion. So this assumption breaks down. Essentially, I disagree with the Hubble site. I think the big rip would stop at the length scale roughly where the 'uniformity' assumption fails. I realize this means I'm disagreeing with actual experts, when I'm a novice. Am I becoming a complete crackpot here? Or is the expert analysis actually flawed like I am suggesting? Can you please ask an astronomer for me?
- John (age 21)

Aha, after reading that Wikipedia article (The Hubble site is misleading in this regard.) I realized that "the big rip" does not refer to the standard picture of fixed (w=-1) dark energy density  gradually becoming more important than matter density but rather to a picture of  increasing (w<-1) dark energy density. ( It also looks like there's an important error on the Wikipedia site. They say that w is a measure of the repulsion, but it is actually a measure of how that repulsion changes as the universe expands, as explained on another Wikipedia article http://en.wikipedia.org/wiki/Equation_of_state_%28cosmology%29. I'll consult with an astrophysicist before making the Wiki modification.)

An accelerating expansion acts like a gravitational repulsion between parts of space. If the strength of that acceleration increases without limit (as in the big rip scenario) it will be able to dominate even local forces, ripping things apart, just as the current weak acceleration tears apart larger-scale clusters weakly bound by gravity.

A fixed dark energy density remains too weak to overcome ordinary local binding forces, as you note. However, it also leads to a boring near-empty flat space in the long run, since even things that collapse into black holes will ultimately  turn into Hawking radiation.

Mike W.

(published on 04/06/2011)

Thank you for replying, but your answer doesn't make sense to me. For your stance to make sense, the total thermal energy in the earth would have to be greater than ALL the gravitational binding energy (let alone ALL the electric binding energy) of the constituent particles. I really can't believe that is the case. Also what you describe sounds like an exponential decay process, yet the 'big rip' wikipedia article says this expansion will accelerate such that the rip will happen in a finite time. None of these things seem to fit together. Is there an astro-physicist friend you can forward this question to? It would be nice to see another take on this.
- John (age 21)

John- You make some good points. Based on your first question and the Hubble site, I'd assumed that the  "big rip" was supposed to be ordinary accelerating expansion with fixed dark energy density (w=-1). However, according to the Wikipedia article it refers to hypothetical w<-1. The answer above has therefore been modified.

I'll try to find an astrophysicist to see whether the (now removed) argument about decreasing cluster density trickling down to decreasing densities at lower scales was correct. The relevant total thermal energy for determining whether dissociation is possible is not, however, the energy in some particular cool object (like the earth) but rather the average over all the matter and radiation. Around here, that would be dominated by the sun, including the nuclear energy that's going to turn thermal in the future. Again, there's general agreement that in the long run (assuming continued expansion) even black holes will turn into thermal radiation, without violating any conservation laws.

Anyway, thanks for catching my sloppy interpretation of the question and my possibly sloppy argument.

Mike W.

(published on 04/09/11)

If the relevant thermal energy is "the average over all the matter and radiation", then asking if the Earth's thermal energy is enough to dissociate it would actually be an over-estimation of the thermal energy available, since the average over all matter and radiation should be the 2.7K cosmic background right? Anyway, I thought about this some more and have another 'counter-example' for the big rip ending. When the rip becomes on the scale of a nucleon, trying to rip apart the quarks will create a huge outpouring of QCD production ... in essence taking the energy density in the 'dark energy' and converting it to a matter explosion, and thus shifting the equilibrium away from the 'big rip' finality. So in addition to my complaint about the isotropic assumption failing well before atomic distances, the radiation death scenario seems possibly only if forces fall off with distance which isn't true for QCD.
- John (age 21)

The issue you raised before was a bit different: whether actual conservation of total energy was consistent with that dissociation. Any finite temperature above zero, no matter how low, is sufficient to dissociate anything in the limit of low density, for which an infinite amount of energy is available per particle.   However, the time scale would be extraordinarily long since not only is the temperature currently low, but it's dropping as the universe expands. At any rate, I now believe that whole discussion was off-topic, since in a fixed-acceleration picture that's not the path that would be taken toward a flat almost empty universe. In a big-rip picture with growing acceleration it's also irrelevant since the tidal pseudo-forces rip everything apart when they become strong enough.

With regard to the interesting question you raise about QCD, here's a tentative first thought. Remember that this big-rip picture involves an increase in the dark energy density without limit.  That includes going past the finite energy density of a quark soup. So I suppose there would indeed be a phase transition as the quarks deconfined, but infinity still beats any finite number.

If some more knowledgeable  colleague corrects that, we'll update. Meanwhile, for anyone who stumbled into this discussion I should include a reminder that this big-rip picture is not conventional and has no obvious physical underpinnings. I guess people are exploring it because it's consistent with data on the past acceleration of the universal expansion. The more standard, and more justifiable, picture with a fixed dark energy density is also fully consistent with the data.

Mike W.

(published on 04/09/11)