# Flattening out the curves.

1. Mar 31, 2004

### Mike2

Does GR say that the expansion of the universe must exist?

Would this mean that there is a tendency to flatten out the curvature of space?

Would this imply that massive objects attract each other in an attempt to flatten out the space between them?

Does higher curvature represent a higher energy state? And is expansion a tendency to move towards a lower energy state?

Thanks.

2. Mar 31, 2004

No........

3. Apr 1, 2004

### Mike2

Then what was all that about Einstein's cosmological constant. He thought the universe was static and gave a constant to ensure that. Then when Hubble discovered that the universe was expanding, they had to readjust the cosmological constant. In doing so, doesn't that say that there is a mathematical necessity for the universe to expand?

4. Apr 1, 2004

Staff Emeritus
EInstein's original equations without the constant predict a universe expanding at a steady rate. The constant allows different types of behavior depending on its value. The original one was tuned to keep the universe a constant size. The current one is tuned (among many other suggestions) to make the universe expand at an accelerated rate.

5. Apr 2, 2004

### EL

Does it? I thought it was dependent on the initial values.
That is, we can observe that the universe is expanding, but what EE tells us is really what will happen given that fact. And doesn't EE (without cosm const) say that the expansion rate will slow down (how much depending on the density of the universe)?

Last edited: Apr 2, 2004
6. Apr 2, 2004

Staff Emeritus
You are right, I misspoke, the universe could shrink to an infinite density as well as expand, based as you said on the density of matter at one point. The point I was making is that is couldn't be static, and Einstein found he could force it to be static by adding a suitable constant multiple of the metric tensor to his gravitational tensor. In MTW's notation $$\mathbf{G} + \mathbf{\Lambda g} = 8\pi \mathbf{T}$$.

7. Apr 2, 2004

### Mike2

OK, are you saying that EE excludes any possibility of a static universe, no condition is ever allowed where there is no expansion, or no contraction? Does this mean that the universe must continue to expand because it can never have a static condition even for an instant as its expansion reverses?

Thanks.

8. Apr 2, 2004

### EL

No, if you include the cosmological constant, EE does not exclude a static universe. Instead it is observations that rules ut that possibility...

No. Even if the cosmological constant is not included.
At the moment the expansion reverses (if that moment will exist, resent observations points in the other direction) it's true that the expansion rate is zero, but the derivative of the expansion rate is not, so it's really not static.
(Compare with the top position of a ball thrown straight up in the air.)

9. Apr 2, 2004

### Mike2

However, there is no alternative to expansion at the beginning, for you cannot contract from a singularity. If you are at the bottom, your alternatives are to stay static (this is excluded) or go up. So it seems that there is no alternative but that the universe expand at the beginning, right?

10. Apr 3, 2004

### EL

The fact that the universe starts from a singularity which expands is just an initial value for the EE.
However observations point out that these are likely initial conditions.
EE just tell us what will happen given initial values.

But I agree that EE together with observations justify the "Big Bang".

11. Apr 3, 2004

### Mike2

Does GR exclude the possiblity of a static universe? I believe the answer would either be yes or the answer would be no.

Would a singularity constitute a static condition? I believe the answer would either be yes or no.

12. Apr 3, 2004

### EL

No. (As was said before.)

I'm not sure how to interpret this question.

13. Apr 3, 2004

### Mike2

You declared that it was allowed to be neither expanding or contracting as long as it was at an unstable equalibrium point, "Compare with the top position of a ball thrown straight up in the air."

That's not what I"m asking here. I'm am comparing with the static condition of resting on a surface, not being thrown in the air, as it were.

Beside the fact that something coming from a nothing, a singularity point, is by definition expansion, I'm asking now if GR requires initial expansion.

Thanks

14. Apr 4, 2004

### EL

No I didn't. I said that EE allow a static universe, if you include the cosmological constant in the equations. Then I said that even if the CC wasn't inluded it is still possible that the expansion rate momentanously can be zero, at the "turn around" moment, since this isn't a static state.

I have never heard that definition of expansion.
No, GR does not require an initial expansion. GR does not require that the universe started from singularity.
GR does not require singularities to expand.
(But if our universe started from a singularity it's quite obvious it has expanded, otherwise there wouldn't be any universe to speak about...)

15. Apr 4, 2004

### outandbeyond2004

What I am about to write is not exactly technical, but a Big Bang singularity is not the same as a blackhole singularity. Also, GR permits a whitehole, which is essentially a blackhole running in reverse. Hope that helps.

16. Apr 4, 2004

### Mike2

OK then, IF WE EXCLUDE THE CC, does GR predict an initial expansion coming from a singularity?

17. Apr 4, 2004

### outandbeyond2004

Mike, I would say GR does NOT predict an initial expansion from a singularity, generally speaking. Perhaps the answer that you are looking for is that special initial conditions are required for expansion. Initial conditions can always be found so that only contraction results. (Some readers may need this explanation: The Einstein field equations are a set of partial differential equations. To find a particular solution, you need a set of initial conditions, symmetry conditions, or some other set of conditions.)

18. Apr 4, 2004

### EL

My answer would be: No, not in general. It depends on the initial conditions.
Although speaking of initial conditions for a singularity is not a trivial task (at least not for me).

It's like holding a ball in your hand and asking if Newtons equations predict that the ball will move upwards.
It depends on if you give it an initial speed upwards or not...

19. Apr 6, 2004

### Mike2

I though you said that barring the CC of EE that it cannot remain still for any length of time. So if it cannot contract because it is already contracted at the beginning, then it must expand, right?

20. Apr 6, 2004

### outandbeyond2004

I would tremblingly venture the opinion that even with a large CC, initial conditions could be found such that the Einstein field equations predict collapse to a singularity. However, I believe that if such were found, most scientists would dismiss them as as extremely unlikely.