# Fate of largest scale structures?

In $\Lambda\mathrm{CDM}$, structures form "bottom up" with larger structures forming later. Structures are generally speaking supported by the velocity dispersion of their constituent objects (e.g. elliptical galaxies are supported by velocity dispersion of stars while galaxy clusters are supported by velocity dispersion of galaxies)$^1$. More massive virialized structures require higher velocity dispersions to support them. What happens when the velocity dispersion required to support a structure becomes relativistic and eventually exceeds $c$? Does the structure simply fail to collapse? Collapse to a black hole? Something else?

It occurs to me that the $\Lambda$-driven exponential expansion that is currently thought to be getting under way in our universe might be rapid enough to cut off structure collapse at some scale, avoiding the scenario I described above. For the purposes of this question, let's assume for convenience a model where the Universe continues to expand with $\lim_{t\rightarrow\infty}\dot{a}(t)=0$.

$^1$ With the notable exception of systems where dissipation is important, allowing the formation of a rotationally supported disk.

• Very interesting question. Can you point me at some literature on virialized LSS so that I can form an opinion? I'm not an astrophysicist by trade, but this sounds like a great thought experiment! Dec 28, 2014 at 22:08
• So, you're asking this for $\Lambda CDM$ minus the $\Lambda$ part? Also, have you heard of Jean's length or Jean's mass?
– Jim
Mar 11, 2015 at 17:42
• @JimdalftheGrey I have heard of Jeans length/mass, but I suspect that starts to break down when the dynamics of the system are approaching the relativistic limit. And I'm asking for... I guess LCDM without the L is a good description. Basically assume the Universe stays matter dominated for a long time instead of switching to $\Lambda$-dominated. Mar 11, 2015 at 19:22
• As $\dot a(t)$ approaches 0, the size of the observable universe grows asymptotically approaching $c$. Since there is an average density of matter and since the expanding edge of the observable universe will encompass more and more mass, at some point the Schwarzschild radius of the mass in the observable universe will be equal to or greater than the boundary of it. It's extremely difficult to say what will happen in this case because every point in the universe would essentially be the center of a black hole. Think about that scenario long enough and you go cross-eyed
– Jim
Mar 11, 2015 at 20:28
• The expansion is slowing, but the size of the observable universe is determined by how far light can reach. If the expansion slows, light can go farther, so the observable universe grows at a rate that approaches the speed of light. The density drops by more and more slowly. The Schwarzschild radius for a region of uniform density is proportional to the enclosed mass, which is proportional to the cube of the radius enclosing. The density of matter falls like $1/a^3$. Thus, the fall in density slows while the rise in mass accelerates. The scenario is unavoidable
– Jim
Mar 11, 2015 at 21:05

This question cannot be answered objectively:

(1) Am I right that you are assuming a "static universe" with lambda to zero? That also means that you neglect Hubble constant (accelerated expansion) and ca. 73% dark energy of the LambdaCDM model. Your assumption contradicts reality.

http://en.wikipedia.org/wiki/Lambda-CDM_model

(2) Cold Dark matter is responsible for structures in the Universe, but nobody knows so far what Dark matter really is. Can it move faster than light? Nobody knows.

• A few objections: 1) I think he assumed a non-zero $\lambda$. 2) Is cold dark matter really responsible for large-scale structures? What do you have to support that? Dec 28, 2014 at 22:21
• (1) $\Lambda \neq 0$ I specifically mention $\Lambda$CDM. I do indeed suggest assuming a cosmology that doesn't match observations at the end of the question, but this doesn't contradict anything else I've said. This can still be answered as a thought experiment (or the cutoff on structure formation from $\Lambda$ could be so large it won't affect the answer). (2) Can it move faster than light? I'd suggest that even though we don't know what DM is, we assume for the moment that it obeys the known laws of physics for a massive particle... Dec 30, 2014 at 23:25