# Expansion & Relativity

1. Mar 19, 2009

### TalonD

I've read somewhere in this forum more than once that GR predicts an expanding Universe. So in laymens terms please, what is it in GR that predicts an expansion of the univers?

2. Mar 19, 2009

### Ich

No, GR predicts a dynamic universe, either expanding or collapsing. Or, more precisely, it predicts that a static universe is unstable.

3. Mar 19, 2009

### marcus

Ich is right.

In lay terms. GR is essentially just one differential equation where each side is a tensor--a rather complicated object with many components.

You can greatly simplify the main GR equation by assuming the universe is uniform (which it seems to be observationally at large scale, on average)

Taking matter to be uniformly distributed, and simplifying, the main GR equation boils down to just TWO simple differential equations involving not tensors but just ordinary numbers. Alex Friedmann, bless his soul, discovered how to do this in 1923. It is the root of cosmology which for over 80 years has been studying solutions of these two simple Friedmann equations and matching them up with data.

These two equations govern the time-evolution of a number a(t) called the scalefactor, which gives a handle on size, expansion history, expansion rate. You can think of it as the "average distance between galaxies". We don't know the overall size of the universe, maybe it is infinite and so has no definite size. But we can track the expansion history by plotting a(t).

If you solve the two Friedmann equations you see that a(t) has to be either increasing or decreasing. And the evidence of our senses (redshift) suggests that it is definitely not decreasing. So it must be increasing. And a(t) plugs into all largescale distances. So if it increases then distances are increasing.

In this sense folks can loosely say that the main Einstein GR equation, via Friedmann's simplification, predicts expanding universe (or as Ich said either expanding or contracting but in any case not static.)

Last edited: Mar 19, 2009
4. Mar 20, 2009

### TalonD

ok, so what has me confused is that we have come up with the idea of dark energy to explain the expansion, right? or no? but GR predicts the expansion. So does GR predict the existance of dark energy? or does GR suggest some other mechanism to explain expansion, some geometric reason similar to the way it explains gravity as geometry ?

I don't know enough math to understand the equations. just trying to get a grip on the concepts.

5. Mar 20, 2009

### yenchin

No. Dark energy is not required to explain the expansion, it was proposed to explain the *accelerating* expansion.

6. Mar 21, 2009

### delplace

As explained by marcus, the tensorial equation of Einstein give rise to a dynamic univers and observations showed that we are in an expanding system. A good image you can relate to these complex equations is :
- left side describe acceleration of univers.
- right side describe momentum flux giging rise to deformation and then acceleration.
If you want to have more details, you need to study differential geometry and tensors use. A good introduction is fluid mechanics where the stress tensor works in a same way than energy impulsion Einstein tensor.

7. Mar 21, 2009

### TalonD

ahh! ok, now that makes sense, thanks!

and so GR predicts a non static universe, but predicts that the rate of expansion is steady, not accelerating?

8. Mar 22, 2009

### delplace

just one element, if you take the general relativity equation in the form : c^2 Rij/R - 1/2 gij c^2 = 8 pi G/ Rc^2 Tij; you can see that left side is homogeneous to m.s^-2 and then homogeneous to acceleration. When you solve such equation, it depends on the area you are solving it. In some area you can be steady, it means with no change of velocity value and then no acceleration in other area you can be non steady. Matematically speaking, for such equations, you need to have some informations about what we often call limits conditions.

9. Mar 22, 2009

### Chronos

GR merely indicates it is highly improbable the universe is static. It does not impose linearity, or non-linearity. That component is derived from observation. The 'why' is not particularly important until we measure that component. It's not unlike the speed of light. We know the speed, but not why it is what it is.

Last edited: Mar 22, 2009