Expanding Universe

[freyar]

The maths get complicated rather quickly, and I'm hardly following them, but the contribution that the cosmological constant makes to Einstein's equation of general relativity seems to enter into the equation in a different place than the mass energy tensor. That affects the metric (using, say, the Robertson-Walker line element), and has an effect which is similar to that produced by the mast energy tensor, but still seems to be a different contribution.

Maybe it's the math getting in your way, but the cosmological constant comes into the Einstein equation in precisely the same way as the energy-momentum tensor. It is just another kind of energy (potential), like mass and radiation. That's why it is often called "dark energy." The big question is exactly where that energy comes from or if (big if) the law of gravity is modified (rather than there being extra energy).

Just to skip through some of the other discussion, I don't really think issues of quantum gravity are too relevant to how space expands in the presence of a cosmological constant or other dark energy (though they may be important in understanding why, say, the cosmological constant takes the value it does). The cosmological constant is present in our universe everywhere and shows up in Einstein's equation at each point. In the voids between galaxies, it is the most important type of energy; in galaxies, it is negligible.

The cosmological constant does not directly affect the curvature. It affects the rate of change of expansion - which itself does not necessarily affect the curvature. You can have perfectly flat spacetime expanding at a constant rate, or at an increasing rate, and in both the objects will be moving as if the space is flat! Expanding does not directly imply changing curvature.

I'll nitpick a little. Flat spacetime does not expand. Flat space can expand, which gives spacetime nonzero curvature. And the cosmological constant will certainly contribute to that curvature.

But, in any case - bound states do not expand.

So what is your take on systems like our local group of galaxies falling into the Virgo Cluster?

 

[Chronikoce]

So what is your take on systems like our local group of galaxies falling into the Virgo Cluster?

I believe that in cases of clusters "colliding" they are actually moving through space towards each other. They do not fall into each other due to expansion (expansion would keep them from falling together).

 

[Umbran]

So what is your take on systems like our local group of galaxies falling into the Virgo Cluster?

Well, as I said - gravitationally attracting or interacting does not imply gravitationally bound. Most usually, "gravitationally bound" means "in orbit around/with". Are we *orbiting* the Virgo cluster? No. Then we probably aren't bound to it.

Could some or all of our local group's galaxies end up bound in that cluster? Possibly. But we aren't there yet.

 

[freyar]

I believe that in cases of clusters "colliding" they are actually moving through space towards each other. They do not fall into each other due to expansion (expansion would keep them from falling together).

I don't quite follow your meaning. When a cluster of galaxies collide, the galaxies making them up rarely collide themselves. (The intergalactic gas does pile up and heat up quite a lot.) But, while you're right that the expansion of the universe pushes two clusters apart, they are gravitationally attracted.

Well, as I said - gravitationally attracting or interacting does not imply gravitationally bound. Most usually, "gravitationally bound" means "in orbit around/with". Are we *orbiting* the Virgo cluster? No. Then we probably aren't bound to it.

Could some or all of our local group's galaxies end up bound in that cluster? Possibly. But we aren't there yet.

I'll have to quibble, I guess. I don't think we can say if we're "orbiting" the Virgo cluster since the universe hasn't lived long enough for us to complete a full orbit yet, I believe. But, if our local group can be projected to "fall into" the Virgo cluster, that means we are in an orbit of it. A highly elliptical orbit but certainly an orbit. So am I right in understanding your concern about us and the Virgo cluster just that we have to project forward using a model of cosmology rather than watching something that has already happened?

 

[Chronikoce]

[MENTION=40227]freyar[/MENTION] Yes that is what I mean. The colliding is in quotes because they don't really collide per say. What I was trying to indicate was that it was due to gravitational attraction and movement through space that galaxies approach each other rather than any effects of expansion.

 

[Nagol]

I don't quite follow your meaning. When a cluster of galaxies collide, the galaxies making them up rarely collide themselves. (The intergalactic gas does pile up and heat up quite a lot.) But, while you're right that the expansion of the universe pushes two clusters apart, they are gravitationally attracted.



I'll have to quibble, I guess. I don't think we can say if we're "orbiting" the Virgo cluster since the universe hasn't lived long enough for us to complete a full orbit yet, I believe. But, if our local group can be projected to "fall into" the Virgo cluster, that means we are in an orbit of it. A highly elliptical orbit but certainly an orbit. So am I right in understanding your concern about us and the Virgo cluster just that we have to project forward using a model of cosmology rather than watching something that has already happened?

If the collision is following a non-closed conic like a hyperbolic arc, you are merely colliding rather than orbiting. Sufficient energy remains in the objects to escape becoming bound, no?.

 

[Umbran]

I'll have to quibble, I guess. I don't think we can say if we're "orbiting" the Virgo cluster since the universe hasn't lived long enough for us to complete a full orbit yet, I believe. But, if our local group can be projected to "fall into" the Virgo cluster, that means we are in an orbit of it. A highly elliptical orbit but certainly an orbit.

Remember that hyperbolic orbits are entirely possible - we could just be passing through. And, even if the final result will be a bound state, that state may not yet have been achieved.

I don't expect there to be enough data (what with the distances involved, and the relatively short time human kind has been able to take data) to distinguish between the bound orbit and the hyperbolic orbit cases.

 

[tomBitonti]

A paper which may be on point:

http://arxiv.org/pdf/0707.1350v1.pdf

Cosmological expansion and local physics
Valerio Faraoni∗ and Audrey Jacques†
Physics Department, Bishop’s University
2600 College Street, Sherbrooke,
Qu´ebec, Canada J1M 0C8
(Dated: February 1, 2008)

The interplay between cosmological expansion and local attraction in a gravitationally bound
system is revisited in various regimes. First, weakly gravitating Newtonian systems are considered,
followed by various exact solutions describing a relativistic central object embedded in a Friedmann
universe. It is shown that the “all or nothing” behaviour recently discovered (i.e., weakly coupled
systems are comoving while strongly coupled ones resist the cosmic expansion) is limited to the de
Sitter background. New exact solutions are presented which describe black holes perfectly comoving
with a generic Friedmann universe. The possibility of violating cosmic censorship for a black hole
approaching the Big Rip is also discussed.

Thx!

TomB

 

[freyar]

So am I right in understanding your concern about us and the Virgo cluster just that we have to project forward using a model of cosmology rather than watching something that has already happened?

If the collision is following a non-closed conic like a hyperbolic arc, you are merely colliding rather than orbiting. Sufficient energy remains in the objects to escape becoming bound, no?.

Remember that hyperbolic orbits are entirely possible - we could just be passing through. And, even if the final result will be a bound state, that state may not yet have been achieved.

I don't expect there to be enough data (what with the distances involved, and the relatively short time human kind has been able to take data) to distinguish between the bound orbit and the hyperbolic orbit cases.

I'll take that as an affirmative to my question above, in that case. I do agree that some (expanding universe generalization of) a hyperbolic orbit is possible even with a collision, though the initial conditions seem pretty nongeneric and unnatural. The initial conditions you'd expect is the formation of different galaxies all basically comoving (simply expanding along with the universe) and proper motions developing later as clusters start to form and a gravitational attraction starts. (In a slightly different context, those are basically the initial conditions used to describe cosmic string wake formation, though the existence of such things is speculative.) Anyway, that's beside the point. I think we can agree that hyperbolic orbits are possible, but saying that all systems that (1) experience some cosmic expansion and (2) will collide in the future must be on hyperbolic orbits is not what you're saying now.

I'm also not sure quite what you mean by "the final state being bound but not yet achieved." We're talking about a deterministic system; either the galaxies will be able to escape in the future (unbound) or not (bound). In Newtonian physics, we'd just ask if the total energy is positive or negative. In the absence of dissipation (which should be pretty negligible for galaxies in clusters), that's not something that changes over time.

But I'm not sure there's a lot to be gained by going over this more.

A paper which may be on point:

http://arxiv.org/pdf/0707.1350v1.pdf

Yes, it looks relevant, but I can't really vouch for it without reading it (which I don't have time to do).

 

[Umbran]

I'm also not sure quite what you mean by "the final state being bound but not yet achieved." We're talking about a deterministic system; either the galaxies will be able to escape in the future (unbound) or not (bound). In Newtonian physics, we'd just ask if the total energy is positive or negative.

But, you can only ask that question when you can consider the system to be isolated.

For example, to even the nearest star, our solar system is pretty much a single point object. We can thus consider the internal workings of the solar system to be isolated, and we can ask if the Earth is gravitationally bound to the Sun.

When we start talking about the Local Group and the Virgo Cluster, though, that kid of approximation no longer applies. The Local Group and the Virgo Cluster are not the only clusters in the dance, and none of the clusters are really point objects on the distance scales involved. In an interaction, these clusters can break apart and mix, and parts of them stay bound while parts of them become unbound. Add to that the uncertainties in their motion, and in our mass estimates, and I think we find ourselves in the realm where we should be able to answer the question in theory, but in practice we find our information insufficient to the task.