Expanding Universe

[freyar]

My understanding is that the rate of expansion appears to be increasing?

Yes, that's right. There are a couple of different ways to measure that now.

But, I have always had the same question: At what scale does expansion occur? Uniform expansion implies odd effects in bound systems. On the other hand, non-uniform expansion seems to imply curvature between the expanding regions and the non-expanding regions.

There is curvature anywhere there's matter (or energy), so that's not really an issue. When we say the universe is flat (in space), we mean on average over very very large regions. But there is curvature, for example, around galaxies. In any case, while the average universe is expanding, bound objects, like galaxies are stuck together --- space is not expanding between the stars of our galaxy, for example.

Also, the scale at which gravity still has an effect, say, for a galaxy, is quite large, and never quite goes away - it's just overwhelmed at a distance by the fields from other masses. I don't understand how there wouldn't be an an expansion within some bound system.

You have to be careful what you mean by a bound system, and the statement is a little vague. Consider a galaxy: the stars are "bound" in the sense that they are not moving quickly enough to escape from each other (in the same way that a rocket has to be moving at a certain speed to escape the earth). And there are small galaxies close to our galaxy that are bound in the same way. Even if you applied Hubble's law on these scales, the expansion speed you'd find would be very small compared to the speeds of the bound objects, so it is irrelevant. You'd expect the structure of spacetime in a galaxy to just be that for a bunch of matter in a non-expanding universe.

However, if you are talking about two far-apart galaxies, yes, they can be gravitationally bound in the sense that they will eventually collapse together but still have some expansion in between. For example, our galaxy is expected to eventually fall into (and merge with) the galaxies of the Virgo Cluster, and, in fact, we are moving closer to them. But the overall expansion of the universe isn't entirely negligible when we look at our motion relative to those galaxies, either.

 

[tomBitonti]

Yes, that's right. There are a couple of different ways to measure that now.

There is curvature anywhere there's matter (or energy), so that's not really an issue. When we say the universe is flat (in space), we mean on average over very very large regions. But there is curvature, for example, around galaxies. In any case, while the average universe is expanding, bound objects, like galaxies are stuck together --- space is not expanding between the stars of our galaxy, for example.

You have to be careful what you mean by a bound system, and the statement is a little vague. Consider a galaxy: the stars are "bound" in the sense that they are not moving quickly enough to escape from each other (in the same way that a rocket has to be moving at a certain speed to escape the earth). And there are small galaxies close to our galaxy that are bound in the same way. Even if you applied Hubble's law on these scales, the expansion speed you'd find would be very small compared to the speeds of the bound objects, so it is irrelevant. You'd expect the structure of spacetime in a galaxy to just be that for a bunch of matter in a non-expanding universe.

However, if you are talking about two far-apart galaxies, yes, they can be gravitationally bound in the sense that they will eventually collapse together but still have some expansion in between. For example, our galaxy is expected to eventually fall into (and merge with) the galaxies of the Virgo Cluster, and, in fact, we are moving closer to them. But the overall expansion of the universe isn't entirely negligible when we look at our motion relative to those galaxies, either.

Hi,

For curvature, I was meaning curvature not explainable by gravity, showing up, say, as an extra lensing effect around galaxies, since the transition from no-expansion to expansion seems to occur when moving outward from a galaxy (basically away from clumps of matter to "flat" intergalactic space).

If expansion is allowed between two distant infalling galaxies, won't that add energy? With expansion, when the galaxies finally reach each other, they will be moving faster than if there were no expansion.

Thx!

TomB

 

[Umbran]

For curvature, I was meaning curvature not explainable by gravity

Freyar may correct me slightly but...

No such thing. The expansion we are talking about is a gravitational effect.

Think of it this way - imagine as if the Universe was filled with a very, very thin fog of stuff* that had gravitational repulsion, rather than attraction. Near massive objects (planets, stars, galaxies) you don't notice. The stuff is so very thin, that compared to the local normal mass it just doesn't show up. But out in the deeps, the real deeps, where there's nothing else, that thin fog of stuff dominates. And there is a whole lot of deeps. Lots and lots of deeps. So, overall, in the universe, this thin stuff dominates in the long run.

You don't see any notable different lensing effect. The fog is pretty darned evenly distributed across everywhere - it doesn't clump up with or away from the normal matter, there is no boundary or transition layer we can point to of "here there is expansion, here there is not". You may not be too wrong to really think that the dark energy that does this isn't a separate thing at all, but is associated with space itself. Or you could say that it is as if space expands by default. That's what it does - expands faster and faster, forever. It is only locally around masses where it *doesn't* expand like that, where there is something that halts this larger scale process.


*This is not a fog of physical material, or normal matter with exotic properties. This is just an analogy to grant a visualization that may help with the concept.

 

[tomBitonti]

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.

I guess we need to clarify what we mean by "gravity" as opposed to the metric.

But, if the metric equation applies everywhere, won't that produce an effect even at small scales (since the equation applies everywhere). Though, since the effect is so very small at those small scales, does that mean that there is no effect (truncate to zero), or does the effect occur probabilistically, with there being a chance of the effect occurring as planck scale event just about everywhere, with an average contribution which adds up to match the overall effect implied by the metric equation?

Hopefully I've not butchered that too terribly.

Thx!

TomB

Edit: To make a crude analogy, would this be like putting a rubber band on a rubber surface, then stretching the rubber surface? The band will be pulled slightly as the surface stretches beneath it, with the pull being detectable as an extra force and perhaps a slight stretch of the band, but, since the band quickly reaches a steady state and does not move any further, no energy is added. This presumes some slight friction between the rubber band and the surface, and not that the band is glued to the surface.

Making this more concrete: A neutron orbiting a neutron star at a distance, with the orbit of the neutron slightly larger than it should be assuming just a contribution to the metric from the mass of the neutron star. This would appear as a slight change to the solution to the geodesic equation for the neutron, because the metric is not exactly that given by the star.

 

[Umbran]

I guess we need to clarify what we mean by "gravity" as opposed to the metric.

As my professors would have said, "gravity", when all is said and done, is the effect on objects. Something curves space-time, objects moving in space-time move in accordance to that overall curvature - that is gravity. So, anything that changes the curvature exerts some gravitational effect. It doesn't matter how many terms we are adding up to come up with that final curvature, or where they enter - gravity is what you get when you add them all up!

Thus, the cosmological constant produces a gravitational effect.

You go into speaking about Planck scale effects. I would advise against that. "Planck scale" is a quantum concept. The cosmological constant is a classical concept. We have a real b*tch of a time getting these to work together.

There's an error in thinking about the rubber-band on the rubber sheet - an error of scale. If you are using the rubber-sheet analogy for the expanding universe, then material objects like galaxies are point objects, not extended things lying on on the surface of the sheet.

Making this more concrete: A neutron orbiting a neutron star at a distance, with the orbit of the neutron slightly larger than it should be assuming just a contribution to the metric from the mass of the neutron star. This would appear as a slight change to the solution to the geodesic equation for the neutron, because the metric is not exactly that given by the star.

Well, remember - space can expand without the dark energy. Dark energy affects the rate of change of expansion. So, it isn't that the neutron would be at point A with Dark energy, but point B without it. It is about how the position of that neutron would change over time. Right now, the orbit is at point A. At some time later, the neutron would be at Point B or Point C, depending on the rate of expansion.

Freyar and I seem to differ a bit on this point - gravitationally bound systems are not a vague concept to me, but a very specific one. "Gravitationally bound" and "gravitationally interacting" are not equivalent. Bound systems don't expand, by definition. The cosmological constant does not change this - if the things are bound, the distance between them isn't going to increase with time.

The thing to remember is that a bound system doesn't just have the mass-energy of the objects, and the kinetic energy of motion. It also has a binding energy, just as an electron in an atom has an energy of binding to the nucleus. That biding energy, like any energy (like, say "dark energy") *changes* the spacetime metric locally, such that expansion does not occur. That's why I say it is part of the definition of a bound state.

 

[tomBitonti]

As my professors would have said, "gravity", when all is said and done, is the effect on objects. Something curves space-time, objects moving in space-time move in accordance to that overall curvature - that is gravity. So, anything that changes the curvature exerts some gravitational effect. It doesn't matter how many terms we are adding up to come up with that final curvature, or where they enter - gravity is what you get when you add them all up!

Thus, the cosmological constant produces a gravitational effect.

You go into speaking about Planck scale effects. I would advise against that. "Planck scale" is a quantum concept. The cosmological constant is a classical concept. We have a real b*tch of a time getting these to work together.

There's an error in thinking about the rubber-band on the rubber sheet - an error of scale. If you are using the rubber-sheet analogy for the expanding universe, then material objects like galaxies are point objects, not extended things lying on on the surface of the sheet.



Well, remember - space can expand without the dark energy. Dark energy affects the rate of change of expansion. So, it isn't that the neutron would be at point A with Dark energy, but point B without it. It is about how the position of that neutron would change over time. Right now, the orbit is at point A. At some time later, the neutron would be at Point B or Point C, depending on the rate of expansion.

Freyar and I seem to differ a bit on this point - gravitationally bound systems are not a vague concept to me, but a very specific one. "Gravitationally bound" and "gravitationally interacting" are not equivalent. Bound systems don't expand, by definition. The cosmological constant does not change this - if the things are bound, the distance between them isn't going to increase with time.

The thing to remember is that a bound system doesn't just have the mass-energy of the objects, and the kinetic energy of motion. It also has a binding energy, just as an electron in an atom has an energy of binding to the nucleus. That biding energy, like any energy (like, say "dark energy") *changes* the spacetime metric locally, such that expansion does not occur. That's why I say it is part of the definition of a bound state.

About plank scale ... I was implying a quantum effect. If the effect of expansion is too small to manifest on small scales, because the size of the effect rounds down to zero, must there still be an effect, and if so, how could it manifest, except as small distributed effects that add up in average to the expected effect? Admittedly, totally made up. I'm trying to reconcile the scale at which expansion is measurable with the need to have the expansion have a continuous effect.

For the neutron ... the path that it takes when not subject to forces other than gravity, that is determined by the metric equation. If the metric equation has values which are slightly different because of the cosmological constant, won't the path be different than the path found when the constant is zero?

Thx!

TomB

 

[Umbran]

About plank scale ... I was implying a quantum effect.

Yes, I know. But surely, the way you talk, you understand that we have no recognized and solid transition from general relativity to quantum mechanics!

If the effect of expansion is too small to manifest on small scales, because the size of the effect rounds down to zero, must there still be an effect, and if so, how could it manifest, except as small distributed effects that add up in average to the expected effect?

Ah. You're under the impression that the way to model the macro-scale effect is by a large number of micro-scale events that add up. We don't generally try to handle it that way at the energy levels of normal matter.

If the metric equation has values which are slightly different because of the cosmological constant, won't the path be different than the path found when the constant is zero?

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.

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

 

[freyar]

Sorry for the delay, haven't been able to get back to EN World.

I'm going to agree with Umbran here with just a few re-iterations and additional comments, I think, since he's painted what seems like a pretty clear picture to me.

For curvature, I was meaning curvature not explainable by gravity, showing up, say, as an extra lensing effect around galaxies, since the transition from no-expansion to expansion seems to occur when moving outward from a galaxy (basically away from clumps of matter to "flat" intergalactic space).

Just to repeat what Umbran said as quickly and straightforwardly as possible: in Einstein's general relativity and theories based on it, spacetime curvature = gravity. That's it. Anything else is some other force.

And, now I am called away again. Will finish this later.

 

[freyar]

If expansion is allowed between two distant infalling galaxies, won't that add energy? With expansion, when the galaxies finally reach each other, they will be moving faster than if there were no expansion.

If the galaxies are already infalling (moving toward each other), the expansion can slow that down a little. In the case of our galaxy, we are currently moving away (on average) from the galaxies of the Virgo cluster, but the references I've seen say that (in standard cosmology) we will eventually turn around and fall back into the Virgo cluster due to the gravitational attraction to all the galaxies there. Not sure if that answers your question, but I didn't quite follow it entirely.

Hate to post and run again...

 

[Chronikoce]

Just noticed I'd missed a page in my reading and my points had already been brought up.