The Expansion Tendency of the Universe According to GR

[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.

 

[EL]

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

No...

 

[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?

 

[selfAdjoint]

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.

 

[EL]

EInstein's original equations without the constant predict a universe expanding at a steady rate.

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)?

 

[selfAdjoint]

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 $$\mathbf{G} + \mathbf{\Lambda g} = 8\pi \mathbf{T}$$.

 

[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.

 

[EL]

OK, are you saying that EE excludes any possibility of a static universe

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

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?

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.)

 

[Mike2]

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.)

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?

 

[EL]

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?

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".

 

[Mike2]

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".

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.

 

[EL]

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

No. (As was said before.)

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

I'm not sure how to interpret this question.

 

[Mike2]

Originally Posted by Mike2
Does GR exclude the possiblity of a static universe? I believe the answer would either be yes or the answer would be no.

No. (As was said before.)

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

 

[EL]

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."

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.

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.

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...)

 

[outandbeyond2004]

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

 

[Mike2]

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.

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

 

[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.)

 

[EL]

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

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...

 

[Mike2]

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...

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?

 

[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.

 

[Mike2]

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.

The point is that at the beginning, it already is a singularity. So there is no where else to go but expand. The initial conditions are forced by having no alternative, right? Why is that so hard to understand?

 

[russ_watters]

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?

This is my view: Since a universe with no initial expansion isn't going to ever expand under GR, it could not produce a universe that looks like ours today (it would immediately re-collapse in on itself).

Using GR alone, there must be initial expansion. The universe cannot be static.

Also, at the "turn-around" point, our telescopes would still be peering into the past - so even if we were at the turn-around point, it could not fool us into thinking the universe was static.

Remember guys - we're not starting with initial conditions and trying to predict what the universe would do, we're starting with the result (present observations) and trying to find a theory+initial conditions that make what we see today hapen. So if your theory+initial conditions don't predict what we see today, one or the other must be wrong.

 

[EL]

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?

Well GR only describes gravity. There are other forces too.
I really can't see why GR should predict that a singularity must expand. (It doesn't say that singularities in black holes expand for example, even if it's maybe not correct to compare these two types of singularities.) And in fact I'm not sure if GR is the best way of approaching this problem. It may not be valid under such extreme situations. Maybe stringtheory will give better answers.

 

[EL]

This is my view: Since a universe with no initial expansion isn't going to ever expand under GR, it could not produce a universe that looks like ours today (it would immediately re-collapse in on itself).

Using GR alone, there must be initial expansion. The universe cannot be static.

I disagree (or do not understand you). Why would GR alone (i.e. independently of initial conditions) predict an initial expansion? Certainly there was an initial expansion, but it's not GR which predicts it. GR cannot predict what initial conditions that should be put in. It's a choise we make. Then we use the theory (i.e. a bunch of equations) to see what it predicts.

Remember guys - we're not starting with initial conditions and trying to predict what the universe would do, we're starting with the result (present observations) and trying to find a theory+initial conditions that make what we see today hapen. So if your theory+initial conditions don't predict what we see today, one or the other must be wrong.

Agree. As you say, we have to find both a theory and initial conditions...how come you then say that GR is enough? Or didn't I get you?

 

[Mike2]

So there is a "curvature" of space. Can there also be a divergence of space? Or is this impossible since it would imply the existence of another reference frame with which to compare?

Thanks.

 

[EL]

Mike2, sorry but I didn't understand.

russ_watters, I would be happy for an answer...

 

[Integral]

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

I do not think, as phrased, that this is a answerable question.

GR is a model of the universe created by man, it cannot ever say "MUST".

The correct formulation of this question would be:
"Can GR correctly model an expanding universe?"

We must make observations of what the UNIVERSE is doing. GR can be used to make guesses at what we might observe, it can lead us toward the kind of observations we need to make. But no prediction is an imperative, it is only a guess until verified by observation.

I do not believe that GR is at a point where we can use it to say what MUST happen. We simply do not have enough data to understand the full capability or limitations of the theory. Someday GR may have a similar status as Newtonian Mechanics and Special Relativity, Good as long as you understand the boundaries of applicability. Currently it is very much under development.

 

[Integral]

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

To explore this phase of the universe we need a working theory of Quantum Gravity, we do not have that tool at this point in time.

 

[Mike2]

To explore this phase of the universe we need a working theory of Quantum Gravity, we do not have that tool at this point in time.

OK, assuming only GR and that QM is excluded from consideration for the moment. If, as I'm told, GR, by itself, excluding the CC, predicts that the universe cannot be in a steady state, does this mean that the universe cannot remain a singularity and therefore the universe will expand according to GR model.

 

[Integral]

OK, assuming only GR and that QM is excluded from consideration for the moment. If, as I'm told, GR, by itself, excluding the CC, predicts that the universe cannot be in a steady state, does this mean that the universe cannot remain a singularity and therefore the universe will expand according to GR model.

Go back and read my first post in this thead. We simply do not have the information required to make such statements.