# Accelerating Expansion Threshhold

1. Jan 6, 2009

### tfb

A popular "Science" TV program said "The accelerating expansion of the universe does not apply to structures as small as the Solar System". Why not? Is there a boundary, marker, or distance that limits where the accelerated expansion begins?
Thanks from an humble pupil,
tfb

2. Jan 6, 2009

### Bodicea

Hi another humble student here, and newbie too, so hello everyone

I believe its the currants in a cake thing. The cake will expand whilst baking, but the currants dont. Its the fabric of space that is being pushed and pulled and the solar system is just being pulled along with it, but yet not affected by it.

3. Jan 7, 2009

### granpa

same reason you dont expand.

4. Jan 7, 2009

### geronimo

Ah, from your own frame of reference only, possibly so!

But I too want to know what this mysterious and possibly arbitrary limit or distance marker is. My intuition tells me there is not one but without such a thing the ballon and raisins in cake analogies have reached their limits. New analogy required, please, to lift our thinking to the next level.

5. Jan 7, 2009

### Janus

Staff Emeritus
The "Limit" occurs where the effect of expansion is less the effect of the mutual gravitational attraction of the bodies involved. Thus for our Solar system, our galaxy and even our local group or cluster of galaxies gravity dominates and they do not expand. Clusters of galaxies, on the other hand, are separated by enough distance that the effect of expansion dominates and they recede from each other.

6. Jan 7, 2009

### 81+

It seems to me that our galaxy, and our galactic cluster, has to either be expanding with the rest of the universe or it has to be contracting due to its own gravity. I would vote for our cluster to be expanding. All by itself, as I understand it, our galaxy remains constant in size due to its gravitational force counterbalancing its centrifugal forces due to its rotation. But if space (all of space) is expanding then the planets, stars, etc. in our galaxy are moving farther apart which reduces the gravitatioinal forces and at the same time increases the centrifugal forces.

Frank

7. Jan 7, 2009

Staff Emeritus
While Janus is absolutely right, I would say that more generally, things don't expand when the forces holding them together are stronger than the expansion. For the solar system, it's gravity. For a ruler, it's chemistry. For an atom, it's electromagnetism.

8. Jan 7, 2009

### wolram

My understanding is, EVERY unit of space, (whatever that is), is expanding every where, the space units between the atoms that make up your computer are expanding, but your computer doe's not expand because the atoms are help together with their binding energy,
which is far stronger than any (pressure) exerted by space units expanding.

I think of this like a field of ghost bubbles, each and every ghost bubble is expanding, each and every ghost bubble has a minuscule capacity to move matter, so minuscule that every other force can over come it.

9. Jan 13, 2009

### hellfire

10. Jan 14, 2009

### Orion1

Newtonian cosmological model...

Consider a classical Newtonian cosmological model where the cosmological force is equivalent to the gravitational force:

Newton's universal law of gravitation:
$$F_g = m \frac{d^2 r}{dt^2} = - \frac{G m^2}{r^2}$$

Newtonian cosmological constant force:
$$F_{\Lambda} = m \frac{d^2 r}{dt^2} = \frac{\Lambda m r}{3} \; \; \; \; \; \; \boxed{\Lambda = \frac{1}{dt^2}}$$

Newtonian cosmological force is equivalent to gravitational force:
$$\boxed{F_{\Lambda} = - F_g}$$

$$\frac{\Lambda m r}{3} = \frac{G m^2}{r^2}$$

$$\boxed{\Lambda = \frac{3 G m_u}{r_u^3}}$$

Would such a cosmological model evolve as completely diffuse particles?

Reference:
Classical Newtonian harmonic oscillator - Orion1

Last edited: Jan 14, 2009
11. Jan 15, 2009

### stevebd1

I know that when it comes to calculating distances using redshift, the normal doppler redshift equation can be used for z<0.01 (0.14 Gly), the relativistic doppler redshift should be used for 0.01<z<0.1 and anything larger than z=0.1 should take into account cosmological expansion. For z=0.1, the relativistic doppler redshift equation gives a distance of ~1.3 Gly which is a fair distance before the effects of the cosmological constant kick in (while it could be said that the universe is still expanding within z=0.1, this is not a cosmological effect and more the actual effect of things simply moving away from each other rather than the space between them expanding, though some argue that there is no doppler effect and that all universal expansion is the consequence of space itself expanding).

relativistic Doppler redshift calculator (scroll down)

Cosmological calculator

Last edited: Jan 15, 2009
12. Jan 15, 2009

### Orion1

Cosmological redshift...

FLRW spacetime (expanding Big Bang universe)
Cosmological redshift:
$$1 + z = \frac{a(t_0)}{a(t)}$$

$$r_u = 2 \cdot 10^{26} \; \text{m}$$

Cosmological constant:
$$\Lambda = \frac{1}{r_u^2} = 2.5 \cdot 10^{-53} \; \text{m}^{-2}$$

Cosmological constant solar system experimental limit:
$$|\Lambda_{ss}| \leq 10^{-46} \; \text{m}^{-2}$$

The measurable lower limit cosmological constant range:
$$r_{ss} \geq \sqrt{\frac{1}{\Lambda_{ss}}} \geq 10^{23} \; \text{m}$$

$$\boxed{r_{ss} \geq 10^{23} \; \text{m}}$$
$$\boxed{r_{ss} \geq 1.057 \cdot 10^7 \; \text{ly}}$$

$$\boxed{r_{gc} = 10^{23} \; \text{m}}$$

The greater the distance, the greater the cosmological constant effect.
The greater the cosmological constant magnitude, the greater the local effects on gravitation.

Reference:
Redshift formulas - Wikipedia
General Relativity - pg. 408
Galaxy cluster - Wikipedia

Last edited: Jan 15, 2009
13. Dec 2, 2009

### tfb

Wikipedia is not my idea of a source for ultimate truth. When space expands my ruler also expands. And the raisins and currants in my cake expand. Gravity will work against expansion, locally as appropriate. And even as my atoms expand, tempered by local gravity, I cannot be aware of my local expansion. And that's because my ruler expands.
Howzzat!?
tfb

14. Dec 2, 2009

### sylas

My understanding of the matter is as follows; and I am particularly indebted to Wallace for helping me follow this. (Which is why I voted for him under cosmo in the current PF voting season.) Any errors, however, are my own. I am an egg.

Expansion is not a force to pull things apart. Expansion is simply the motion of things moving apart. Things moving apart from each other are expanding; things not moving apart from each other are not expanding.

The role of "space" is not some kind of fabric or influence that helps moves things around. To get really really simple: it is a name we use for the gaps between things.

The rate at which things move apart from one another (expand) can change over time, because of various forces that may apply. Gravity, for example, tends to pull things back together. If some collection of things is expanding, gravity will tend to slow the expansion down.

The solar system isn't expanding. It is not because gravity is hard at work preventing the solar system from being pulled apart; it is that gravity HAS pulled it together so that there is no expansion going on. Same for our galaxy, or our local group of galaxies. Gravity has pulled them all together so that they are gravitationally bound and not expanding.

A complication is "dark energy". Apparently there is a kind of energy within the vacuum that works a bit like a tiny "pressure" (and that might not be the best word) to push things apart. The tendency of dark energy is to accelerate expansion. So in a sense there is something, it seems, that is continually pushing things apart while gravity is pulling them together. But it is not the expansion that is doing the pushing or pulling. Expansion is just a description of how things are moving at present.

A further complication is that space is not as simple as we once thought. We need to use GR to describe it properly. It has properties... curvature, for instance. On really large cosmological scales, the expansion of the universe looks like an expansion of space itself, and seems to be an almost irresistible thought to think of space carrying all the "stuff" along for the ride. That is, space expands and that is pulling things apart, as if space where some kind of fabric to which "stuff" is attached.

I think a more credible idea is to think of "stuff" as pulling on space, rather than the reverse. As "stuff" moves apart, there's more space.

Cheers -- sylas

Last edited: Dec 3, 2009
15. Dec 3, 2009

### Wallace

Hi Sylas, I'd say you've got a pretty good understanding going there! I have a few comments and additions which will hopefully help.

A key concept here is the Virial Thereom which describes the balance between kinetic and potential energy in a stable system. The systems you mention; galaxies, clusters (eventually) and solar systems are examples of 'virialised' systems in which this balance holds.

The early universe has small differences in density from place to place and you can imagine solving the Friedmann equations, which are normally taken to represent the whole universe, for a finite region which happens to be at a different density from the average. If a region is sufficiently overdense, it will eventually collapse (even if the overall universe does not) forming a galaxy or cluster or galaxies. Formally, the size of the region (its local scale factor) will go to zero at some time. However, the Friedmann Equations are a simplification, and in practice the virial theroem kicks in preventing the contractiong from proceeding once the kinetic and potential energy are in balance.

So, once a system is virialised the initial condition of expansion is 'forgotten' and the system is stable. In practice, the mergers of different systems is actually the cause of the build up of things like galaxies and clusters, rather than isolated collapse, but the same arguements about virialisation hold.

This is not as much of a complication as you might think. The simplest model for dark energy is a cosmological constant in which the energy density of dark energy is constant. In the Newtonian limit this acts as a force which is repulsive and proportional to distance, so that Newton's law of gravity becomes

$$F = -GmM/r^2 + Cmr$$

where the C is some constant. What this does therefore is slightly changes the balance involved in the virial theorem, but importantly there is still a stable balance point. That is to say, in the presence of dark energy, the Earth might orbit a little bit further from the Sun than without, but it still finds a stable orbit. Even in the presence of dark energy, there is no residual expansion in bound systems.

The complication that can arise is the case of dynamical dark energy, in which the energy density of dark energy is not constant. In this case in principle the balance of the virial theorem could change over time, however if the energy density of dark energy is slightly decreasing, then this actually means a virialised system would contract, rather than expand, due to dark energy. In practice, the energy density of dark energy compared to that of matter is very very tiny in a collapsed objects like galaxies and clusters, so you can completely ignore its effects when it comes to internal dynamics. So even in the case of dark energy, there is no expansion in bound systems.

The one exception is the case of 'phantom' dark energy, in which the energy density of dark energy increases without bound into the future. In this case bound systems can be torn apart, and in principle eventually even atoms and smaller particles cannot stay bound, leading to a 'Big Rip'. This is a cartoon model that is completely absurd and most dark energy theorists rue the day this one got into the pop sci imagination, but none the less it can't be ruled out from present observations. Note that even in the most extreme cases, none of this will start happening for Billions of years.

I wouldn't worry too much about that. You can always replace 'curvature of space' with 'gravitational field' (at least in the Newtonian limit) and then things are usually easier to understand. I strongly believe that if you need to invoke GR concepts like 'curvature of space' in order to explain or understand basic concepts to do with the expanding universe then you have missed something somewhere. GR is neccessary in order to get the numbers right, but not the concepts.

16. Dec 3, 2009

### twofish-quant

One other way of thinking about it.....

The first calculation that you do for how the universe behaves *assumes* that the universe is completely even and that matter is totally evenly distributed. You get a nice simple equation which describes the universe is evenly expanding.

Now this is an approximation, so the next calculation you do takes all of the lumpiness in the universe and calculates that as a correction to your first calculation. You get a more accurate answer but the calculation is a lot messier.

Now for things like the solar system where things are not very even at all, the basic assumptions you have totally break down.

One other way of thinking of this is imagine a gas. If you look at a large amount of gas then you can imagine the gas as being a continuous, uniform fluid, and that gets you the right answer if you are looking at large amounts of gas. If you are looking at an one atom, this is not going to work.

17. Dec 3, 2009

### twofish-quant

It's incorrect.

The reason people talk about "expanding space" is that the theory that people use to model gravity involves looking at gravity in terms of distortions in space, but it's really not necessary. You can get the basic picture of the expanding universe by using plain Newtonian gravity without thinking about expanding space at all.

What is going on is that to get the general behavior of the universe, you *assume* that matter in the universe is evenly distributed. Now for the universe as a whole, that's a pretty good assumption. If you look at the solar system, it's a pretty bad assumption.

It's the old physics joke "assume a spherical cow".

Last edited: Dec 3, 2009
18. Dec 3, 2009

### tfb

Please excuse my ignorance. But if ALL RULERS expand, dosen't all the math and theories simply become irrelevant?
tfb

19. Dec 3, 2009

### VooDooX

Question... If the universe is expanding and a photon is on a part of the bit that is expanding would this cause the photon to exceed C? also is it possible for expansion (which i assume is going faster and faster due to as we have more and more space we have more and more space thats expanding it seems it should be exponential ) to exceed C?

20. Dec 3, 2009

### S.Vasojevic

Whole mess is build up on the sentence "space is expanding". For almost all purposes, we can say that space is not expanding, but the galaxies are flying away of each other. As they move further away, there is more space between them by definition, but that does not mean necessary that space expansion is cause, it may very well be only consequence.

Last edited: Dec 3, 2009