Physics Asked by J Kusin on January 3, 2021
My rudimentary understanding of dark energy as the cosmological constant is that the vacuum state of space has positive energy but negative/repulsive gravity/pressure.
Given a system dominated by "positive" gravity like a planet or solar system, "positive" gravity wins out and the system doesn’t expand.
But in deep space is there some sweet spot (or shell) where a system is prevented from clumping purely due to its own rigidity and the negative pressure of dark energy? I’m imagining a thin rigid structure like the edges and vertices of a dodecahedron that dissipates heat outwards and uses the constant negative pressure (a constant force? It is gravity after all right? — it’s part of the curvature of spacetime) to do work and continually repair itself.
Is this structure prevented soley because no material is that rigid and low mass?
A crude answer is "nothing is that big".
The cosmological constant has a value of $10^{-52}$ m$^{-2}$ (in units where $c=1$, so I hope I do this right...). So the approximate linear scale we are talking about before those effects become important is $sim 10^{26} m$. The largest structures in the universe are Galactic super clusters, which are ~millions of light years across. In units of $c=1$, that's
$$sim 10^{6} text{ly}~ c (pi times 10^7text{ s/yr })sim 10^{13}~m$$
($pi times 10^{7}$ is the approximate number of seconds in a year). So if I did that right, the largest structures we know in the universe are about a ten thousand billion times too small for the cosmological constant to play an important role.
Answered by levitopher on January 3, 2021
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