# Centre of mass of universe

1. Dec 21, 2007

### cosmic.ash

Considering a infinite unbound universe in 4 spatial dimensions, could the cosmic expansion be explained if we consider all matter in the universe to be accelerating towards its centre of mass due to its grav pull

Last edited: Dec 21, 2007
2. Dec 21, 2007

### Garth

In an infinite unbounded universe where would the centre of mass be?

Garth

3. Dec 22, 2007

### cosmic.ash

sorry : correction garth,
in an unbounded finite universe (due to curvature of space time as a consequence of GR)
could the cosmic expansion or hubble expansion be explained if we consider all matter in the universe to be accelerating towards its centre of mass due to its grav pull

4. Dec 22, 2007

### Garth

Only in a bounded universe, say a sphere of galaxies in otherwise empty space, could you define a Centre of Mass. This is not a standard model for our universe, of course.

You can however, in an unbounded finite or infinite universe, define a frame of reference that co-moves with the centroid of all the matter in motion within the universe. This is presumably co-moving with the Last Scattering Surface of the CMB.

Cosmic acceleration may be explained by our galaxy being in a huge void so that objects in distant regions from us are being 'pulled' outwards. It would mean of course that would have to be in a 'special' or favoured location', which would be in violation of the Copernican Principle.

Actually you don't need an explanation for the expansion of the universe, it has to either expand or contact, we happen to be in an expanding universe. It is a static universe that would be difficult to explain because it would require some form of specially balanced Dark Energy to hold things static 'in place'.

Garth

Last edited: Dec 22, 2007
5. Dec 22, 2007

### sysreset

Garth can the expansion of space just be a property of space rather than requiring dark energy to propel it?

6. Dec 22, 2007

### Garth

Hi syreser,do not confuse expansion of the universe with the acceleration of the expansion.

As I said there is no explanation, no force, causing the universe to expand, it has to expand or contract, we are in an expansion phase at the moment.

Gravitational forces should cause that expansion to decelerate, however recently it has been discovered that it appears the expansion is accelerating. It is this acceleration that requires Dark Energy, which has the property that its pressure is negative.

Garth

7. Dec 23, 2007

### sysreset

Garth, I can see that Dark Energy can act on objects with mass and cause them to accelerate apart from each other. What I cannot understand is why you need Dark Energy to accelerate the expansion of space itself. We have already established that the expansion of space does not require the input of any energy; it is simply a property of space that it expands. Shouldn't this also apply to the acceleration of the expansion of space?

I am trying to distinguish between acceleration of objects in space, versus the acceleration of expansion of empty space.

8. Dec 23, 2007

### Garth

Throw a ball into the sky, under gravity its velocity decelerates and eventually will fall back to Earth.

Throw it hard enough, above escape velocity, and it will decelerate but never fall back to Earth.

If you saw a rising projectile that was accelerating away from the Earth you would know that it was a rocket or something similar with a thrust propelling it into space.

The universe is "under gravity" and so as galaxies etc. move away from each other under cosmic expansion they decelerate in their motion and may or may not eventually "fall back". That is, the universe's expansion may reverse into a contraction, depending on the strength of the cosmological gravitational field. This depends on whether the average density of matter and energy in the universe is greater or less than the critical density.

Positive pressure within the universe acts as extra energy and increases the deceleration. However surprisingly it appears the universe is accelerating in its expansion, this requires a "thrust" of some kind.

Rather than strapping rocket engines to all the particles in the universe, it makes more sense to conclude that there is a form of negative pressure that reverses the deceleration into an acceleration, this negative pressure is provided by Dark Energy that comprises 73% of the mass content of the universe.

This is the present accepted mainstream $\Lambda$CDM model.

Garth

Last edited: Dec 23, 2007
9. Dec 25, 2007

### sysreset

Garth, I'm not going to let you off the hook that easy!

You said that there is "no force causing the universe to expand, it has to expand or contract, we are in an expansion phase." Expansion is just a property of space, not evidence of a force, which I agree with.

Yet there have been and will be other phases in which expansion of space is either faster or slower than it is now, and that expansion is still just a property of space, not evidence of a force.
So logically, an acceleration of expansion, or a deceleration of expansion of space would not imply the presence of a force either. Remember, I am only talking about expansion of empty space, not the movements of galaxies. I am not disputing the presence of gravity (which would move galaxies toward each other) or Dark Energy (which would move galaxies away from each other.

10. Dec 25, 2007

### Garth

What I am talking about are solutions of Einstein's field equation in the cosmological case.

The behaviour of the expansion of the universe can be compared to Newtonian motion in order to understand what is going on and to see how Newtonian gravity melds with GR under certain circumstances, but Newtonian theory is limited and there are differences.

One such difference is the fact that in GR the presence of positive pressure causes a deceleration not acceleration of the expansion.

Remembering that gravitational accelerations are interpreted in GR as the effect of the curvature of space-time and not an actual force, nevertheless, in the absence of pressure, the expansion of the universe can be described in a Newtonian kind of way.

In Newtonian gravity velocity does not have to be explained, no force is necessary to keep the planets moving on their orbits, on the contrary it takes a force to slow them down or speed them up!

In a similar way the universe just expands, and if it were empty it would expand at a constant rate - the Milne model.
It does take a force to decelerate the expansion, just as it does to slow down a moving object such as that provided by the brakes on a car, and it is the cosmological gravitational field generated by the mass and energy within the universe that provides such a force to decelerate the cosmic expansion.

However, as I have said, in its recent history (since z ~1) the universe appears to have been accelerating in its expansion. This too requires a force, such as that provided by the negative pressure of Dark Energy.

There is one caveat, I have said Newtonian physics is only a limiting case of GR and it has its limitations when used to understand how GR works; another difference is that the GR field equation contains an undetermined constant, the cosmological constant $\Lambda$. If this constant does exist and is positive then it would cause the expansion to accelerate without a 'force', for that acceleration would simply be a property of gravity at cosmological ranges.

An important difference between the cosmological costant and DE is that $\Lambda$ has to be constant, whereas DE might evolve with time.

Garth

Last edited: Dec 25, 2007