It seems to be said, fairly often, that "gravitationally bound objects experience no expansion of spacetime". For example, the incessant "stretching" of Spacetime does not "rip apart" our Solar System, nor our Galaxy, nor our Local Group. So, once a "glob" of matter becomes "gravity bound", the Spacetime it occupies (apparently) stops "stretching", and "freezes out" of the background Hubble Expansion.

 

It is my understanding, that current computer simulations assume, for simplicity, a uniform "background" expansion rate, which uniformity they then "force" upon, & across, the whole simulation volume. It is under such simulated conditions, that "Dark Matter" is necessary, to keep confined all the baryonic matter.

 

But, if it is true, that the Spacetime around gravity-bound objects stops stretching, then wouldn't "artificially forcing" a uniform stretching of Spacetime across the complete computational volume, including in particular the Spacetime occupied by said gravity-bound object, amount to imposing a false & fictitious force of "anti-gravity", which would work (errantly) to "rip apart" those objects in the simulations (making it look like more (dark)matter was needed) ??

 

What part of the picture am I misunderstanding ??

 

It is my understanding - remember I am new to this - that the space/time is expanding and since "gravitationally bound objects" are sitting in the same "gravity well" they move with the space/time but are not stretched with it because the warping of the space/time by their mass is not increased (the well stays the same size while moving).

Is it wrong that I thought that you were asking how Expansion Packs for The Sims work?

Here is possibly how.

 

http://astronomy.swin.edu.au/sao/guest/knebe/

According to Carroll & Ostlie's Introduction to Modern Astrophysics, Birkhoff's Theorem can be written in the form:

 

[math]\frac{d^{2}R}{dt^{2}} = - \frac{4 \pi G \rho R}{3}[/math]

 

Thus, this might mean, that every "cell" (x_ijk) in the simulation would have it's own Scale Factor (R_ijk). If so, cells that started off over-dense, would gravitationally contract more, whilst expanding less, "doubly" boosting their (Over-)Density Contrasts.

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According to Wikipedia, the "Birkhoff's Theorem equation" (as it were), with a Cosmological Constant ([math]\Lambda[/math]), and gas pressure term (p), is: