# Does the expansion of spacetime affect gravitationally bound object?

Quick question on cosmology. As everyone knows, the expansion of spacetime increases the distance between galaxies. However, I'm wondering if the same expansion increases the distance between stars in any specific galaxy. I vaguely remember my cosmology professor saying that this does not happen since the stars in any individual galaxy are "graviationally bound" (but as I said I remember vaguely, so tell me if this is wrong).

So my question is: does the gravitational attraction between stars in our galaxy negate the effect of expansion completely, or merely diminish it so that it is not as easily detectable?

## Answers and Replies

To notice any effect of expansion one must observe galaxies beyond our own local cluster. M31 for example is actually blue shifted wrt the Milky way. To find out the point between any two masses as to where the G force balances the stretching of space - you need to know the masses of the objects, and the separation distance.

To notice any effect of expansion one must observe galaxies beyond our own local cluster. M31 for example is actually blue shifted wrt the Milky way. To find out the point between any two masses as to where the G force balances the stretching of space - you need to know the masses of the objects, and the separation distance.

I see. So then, the gravitational force can negate the effect of expansion. I think this answers my question, thanks a lot.

pervect
Staff Emeritus
Quick question on cosmology. As everyone knows, the expansion of spacetime increases the distance between galaxies. However, I'm wondering if the same expansion increases the distance between stars in any specific galaxy. I vaguely remember my cosmology professor saying that this does not happen since the stars in any individual galaxy are "graviationally bound" (but as I said I remember vaguely, so tell me if this is wrong).

So my question is: does the gravitational attraction between stars in our galaxy negate the effect of expansion completely, or merely diminish it so that it is not as easily detectable?

This has been discussed here before, but my favorite FAQ entery is http://www.astro.ucla.edu/~wright/cosmology_faq.html#SS

Basically, the effect on the solar system is negligible. The effect on galaxies is also unmeasurably small. The FAQ focuses on the solar system, though.

The case which maximizes expansion is the case when dark matter is assumed to be leaving the galaxies at some constant rate due to the expansion. You then basically have a tiny effect on the size of the galaxies due to the resulting mass loss.

If you make different assumptions, you can even get zero change in size of the galaxies due to the expansion. For instance, a circular orbit around a body in a Schwarzschild-De-sitter space does not change in radius as time progresses, even though the De-sitter space is "expanding" exponentially.

This has been discussed here before, but my favorite FAQ entery is http://www.astro.ucla.edu/~wright/cosmology_faq.html#SS

Basically, the effect on the solar system is negligible. The effect on galaxies is also unmeasurably small. The FAQ focuses on the solar system, though.

The case which maximizes expansion is the case when dark matter is assumed to be leaving the galaxies at some constant rate due to the expansion. You then basically have a tiny effect on the size of the galaxies due to the resulting mass loss.

If you make different assumptions, you can even get zero change in size of the galaxies due to the expansion. For instance, a circular orbit around a body in a Schwarzschild-De-sitter space does not change in radius as time progresses, even though the De-sitter space is "expanding" exponentially.

That's very interesting, thanks. Incidentally, perhaps you could refresh my memory. Is a De-Sitter space the one where the scale factor goes as eH*t?

pervect
Staff Emeritus
That's very interesting, thanks. Incidentally, perhaps you could refresh my memory. Is a De-Sitter space the one where the scale factor goes as eH*t?

Yep - that's the one. It arises when you have a cosmological constant.

If you have a de-Sitter space-time, and you have a single massive object in it, you have the Schwarzschild de-Sitter metric I was talking about.

See http://arxiv.org/abs/gr-qc/0602002v2 for more details.

If you put an object into a circular orbit in this space-time, the radius of the orbit is a constant - i.e. it's a true circular orbit, r does not change as a function of time.

Chris Hillman
Quick question on cosmology. As everyone knows, the expansion of spacetime increases the distance between galaxies. However, I'm wondering if the same expansion increases the distance between stars in any specific galaxy. I vaguely remember my cosmology professor saying that this does not happen since the stars in any individual galaxy are "graviationally bound"

Right, this is discussed in MTW and other standard sources. A good place to start, in fact, might be the FAQ http://math.ucr.edu/home/baez/physics/Relativity/GR/expanding_universe.html. This topic has been discussed in sci.physics.research at various times; until the past few years, this newsgroup (now largely overrun by cranks) was often a reliable source of information, so you can try http://groups.google.com/group/sci.physics.research/browse_thread/thread/7e26f7eb06749561/ and http://groups.google.com/group/sci.physics.research/browse_thread/thread/b4c8e98f4c5f8b6b/
In addition, see http://www.arxiv.org/abs/gr-qc/0508052 and
http://www.arxiv.org/abs/gr-qc/0612146.

So my question is: does the gravitational attraction between stars in our galaxy negate the effect of expansion completely, or merely diminish it so that it is not as easily detectable?

The latter. Finding the locus where the transition from "Sun dominated" to "Hubble dominated" occurs for our solar system is a good exercise (see the paper by Price cited above). Another good exercise is to figure out whether this alone can account for the so-called Pioneer effect (assuming this has not be misinterpreted, or is not accounted for by even more mundane physics than the Hubble expansion).

About the Schwarzschild-de Sitter lambdvacuum: somewhere or other I have posted a very detailed analysis using effective potentials of test particle motion in this solution, including the issue of stability. Among other things, this affords a fun demonstration of using Sturm chains to analyse the disposition of real roots! There are also some arXiv eprints which carry out a similar analysis.

Getting a bit off topic, but here's another great exercise involving the de Sitter and Schwarzschild-de Sitter lambdavacuums: find as many "interesting" coordinate charts as possible and interpret the geometric/physical meaning of the coordinates.

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