# Why galaxies are not expanding

#### Chalnoth

Science Advisor
So (IMHO), the various answers depend on the question being asked:
* Is space in a gravitationally bound system expanding? Yes.
No, it isn't. I'm reasonably certain that this has been experimentally demonstrated using laser ranging experiments, though my Google-fu is failing me at the moment.

The calculations that result in some expansion basically assume the expansion. They don't derive it.

#### andrewkirk

Science Advisor
Homework Helper
Gold Member
If the expansion comes from a nonzero cosmological constant $\Lambda$ then the answer to the question is quite clear - the configuration of stars within a galaxy will be very slightly different from what it would be if $\Lambda=0$. One would intuitively expect that difference to be that the radius of the galaxy stabilises at a slightly larger distance than would occur if $\Lambda=0$. But it may be that with some peculiar-shaped galaxies that does not occur, because of the way interactions play out under the field equations.

But in every case, the configuration of stars in the galaxy will be determined by Einstein's Field Equation $G+g\Lambda=T$, which operates everywhere in spacetime, so it must be the case that a nonzero $\Lambda$ changes things.

If cosmological expansion is instead caused by something that is not constant, such as quintessence or moduli, the answer is 'who knows'. These fields vary over time and space so their effect within a galaxy will depend on the strength and configuration of the field within that galaxy.

#### Mark M

"dark energy....That's a general relativistic effect caused by an even distribution of matter. The solution of the Einstein Field Equations that is homogeneous and expanding is the FRW metric. However, the FRW metric only applies for homogeneous distributions of matter, which a galaxy is not. Instead, the Schwarzschild metric is used inside of a galaxy, where space isn't expanding."
Naty, the part you left out was important. Normal expansion is an effect of general relativity, not dark energy. Dark energy 'piles on' and accelerates the normal, general relativistic expansion of the FRW metric. Normal expansion is a feature of the FRW metric, whereas dark energy is a constant force you must factor in.

That's why I stand by what I said in that thread. Normal expansion due to the FRW metric applies only to intergalactic space. However, dark energy has a slight effect inside of galaxies. That's because it's included in the Einstein field equations in the form of a cosmological constant. The EFE govern gravitational interactions everywhere, so we can naturally conclude that dark energy has a slight effect everywhere.

#### Naty1

MarkM:

Normal expansion due to the FRW metric applies only to intergalactic space. However, dark energy has a slight effect inside of galaxies.
Yes, in general I like that explanation and above all it IS logical. And two guys here I respect seemed to agree in another thread....

But I also keep an open mind because I don't understand how 'a' evolves within a
gravitationally bound system and am not sufficiently conversant in all the mathematical assumptions to know what models apply and what ones weaken at such miniscule calculational distances:

When Wallace says emphatically:
.....The metric in the region of bound structure looks nothing like the FRW metric, in particular it has no global time dependence (though will of course evolve).
...I have to wonder about the effect.
Wallace is apparently a practicing cosmologist so I put considerable weight when he make a strong point as in that quote.

and I like phinds comment:
....but the amateur physicist in me says negligible and zero are radically different, so it matters a lot.

#### andrewkirk

Science Advisor
Homework Helper
Gold Member
I don't understand how 'a' evolves within a gravitationally bound system
This question has no answer because 'a(t)' is a parameter of the FLRW model, which does not apply within a bound system such as a galaxy. Asking what the FLRW 'a' is inside a galaxy would be like asking what is the radius of an ellipse.

The FLRW model assumes perfect homogeneity of the universe, but a galaxy is by definition a region in which the homogeneity assumption does not apply.

The question we can ask, that does make sense within a galaxy, is:

'What effect do the factors that make the universe's expansion accelerate have within a galaxy?'

The answer to that is most likely reached via analysis of the impact of a nonzero $\Lambda$ on the curvature of spacetime within a galaxy. My facility with tensor equations is regrettably way below the level necessary to answer that question. But it seems reasonable to be confident that the answer is not 'none whatsoever'.

#### Chalnoth

Science Advisor
This question has no answer because 'a(t)' is a parameter of the FLRW model, which does not apply within a bound system such as a galaxy. Asking what the FLRW 'a' is inside a galaxy would be like asking what is the radius of an ellipse.

The FLRW model assumes perfect homogeneity of the universe, but a galaxy is by definition a region in which the homogeneity assumption does not apply.

The question we can ask, that does make sense within a galaxy, is:

'What effect do the factors that make the universe's expansion accelerate have within a galaxy?'

The answer to that is most likely reached via analysis of the impact of a nonzero $\Lambda$ on the curvature of spacetime within a galaxy. My facility with tensor equations is regrettably way below the level necessary to answer that question. But it seems reasonable to be confident that the answer is not 'none whatsoever'.
Oh, yeah, the effect of dark energy on galaxies is most definitely not zero. It's small, but not zero. The effect is even measurable for large galaxy clusters:
http://en.wikipedia.org/wiki/Sachs–Wolfe_effect

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