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i am not sure i used the correct formulization so be crative.

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- #1

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i am not sure i used the correct formulization so be crative.

- #2

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I'm sorry, but I can't give any more detailed answer than this. I'm not so good with this. :P

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i am not sure i used the correct formulization so be crative.

In the Newtonian framework. infinite space causes paradox!I think.your argument is absolutely

right!but,If you change your view a little, still in Newtonian framework,you will get an contracting universe!just imaging a sphere in space ,and the outside mass can not affect the physics inside.and you can figure out that the length is contracting! no matter how big your imaginary "sphere" is!this is a paradox!this means Newtonian view point should have some thing wrong.

Einstein gives the answer,it is the spacetime itself expanding!So it is ok to have both no force acting on a galaxy for example ,as you pointed out,and the space between galaxies contracting,like the secondary view of Newtonian approach.

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i don't quite understand the paradox you were talking about. why is it contracting?

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- #6

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i am not sure i used the correct formulization so be crative.

The best way to understand this is to imagine an empty sphere. Einstein says, if you insert mass, the space is bent and contracted. This means that the sphere will shrink in size. The space is being pulled in towards the object. If you keep inserting mass into the sphere, then the sphere will keep shrinking. The cosmological constant just represents the ability of the sphere to counter this energy and expand outwards.

Galaxies are so far apart that they don't necessarily attract one another. This is just the inverse square law taking effect.

If you say that the expansion should be slowing down, then you would have to asssume an initial energy, like a bang from a bullet, but no constant acceleration. If you think of the universe this way, then the energy would dissipate due to the stress caused by the mass in the sphere. This is not what we observe. We observe a constant acceleration, which is growing ever more dominate with distance. This is a constant acceleration, hence the cosmological constant.

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We have not determined the ultimate fate of the universe yet, we only have possible ends, and the Big Crunch has not been ruled out yet.

The answer to the end of the universe lies in the value of [tex]\Omega[/tex].

If it is [tex]\Omega[/tex] is greater than 1 then there will either be a the Big Crunch or space and time will continue to expand if there is enought dark energy to cancel out gravity.

If [tex]\Omega[/tex] is less than 1 then Heat Death or the Big Rip is possible.

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We have not determined the ultimate fate of the universe yet, we only have possible ends, and the Big Crunch has not been ruled out yet.

It is however, most unlikely. If the expansion is speeding up, then it is apparent that the dark energy is overpowering the gravitational pull of all of the objects, and it will only continue to surpass the gravitational pull as the distances increase.

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It is however, most unlikely. If the expansion is speeding up, then it is apparent that the dark energy is overpowering the gravitational pull of all of the objects, and it will only continue to surpass the gravitational pull as the distances increase.

What about gravitational backreaction to speed up the expansion?

if dark energy is cosmological constant ,and GR is always right,Ok, ultimate de sitter stage is doomed.

but the two is not exactly confirmed. if dark energy is dynamical ,there is possibility that index of equation of state of dark energy going back to normal in the future. And I don't quite like talking about phantom in FRW cosmology ,I don't think it is right to apply phantom and GR(for freidmann equation) at the same time. If phantom is confirmed ,then GR must be modified.however,I don't know if current observation confirmed the violation of null energy condition.Data fitting toady from supernova or sth just tell the story that the fitter want it to be,in some subtle extend,personally,I think.

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i don't quite understand the paradox you were talking about. why is it contracting?

you'd better refer to a textbook for Newtonian viewpoint 2.

your point,which i call it Newtonian viewpoint 1, can not be found in any book since it is a little heresy , but I agree with you.

you can refer to this one for Newtonian contracting in infinite flat space,which is Newtonian viewpoint2 I mentioned.

Liddle A - Introduction To Modern Cosmology.

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What about gravitational backreaction to speed up the expansion?

if dark energy is cosmological constant ,and GR is always right,Ok, ultimate de sitter stage is doomed.

but the two is not exactly confirmed. if dark energy is dynamical ,there is possibility that index of equation of state of dark energy going back to normal in the future. And I don't quite like talking about phantom in FRW cosmology ,I don't think it is right to apply phantom and GR(for freidmann equation) at the same time. If phantom is confirmed ,then GR must be modified.however,I don't know if current observation confirmed the violation of null energy condition.Data fitting toady from supernova or sth just tell the story that the fitter want it to be,in some subtle extend,personally,I think.

I have to say, there is much of this I am not familiar with.

"the two is not exactly confirmed" Dark energy and General Relativity are pretty darn accurate. Are you suggesting that Dark energy could be something besides a constant? I don't know exactly what you mean here.

I am pretty confident that the theory of gravitational backreaction and dark energy being dynamical is just a way to save string theory, i.e. in compactified D brane cases. If not, I don't know exactly what you're talking about.

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In the Newtonian framework. infinite space causes paradox!I think.your argument is absolutely

right!but,If you change your view a little, still in Newtonian framework,you will get an contracting universe!just imaging a sphere in space ,and the outside mass can not affect the physics inside.and you can figure out that the length is contracting! no matter how big your imaginary "sphere" is!this is a paradox!this means Newtonian view point should have some thing wrong.

Einstein gives the answer,it is the spacetime itself expanding!So it is ok to have both no force acting on a galaxy for example ,as you pointed out,and the space between galaxies contracting,like the secondary view of Newtonian approach.

None of this makes sense to me. First, you never state if there is mass in your imaginary sphere, although I assume there is. Also, what mass is outside of this sphere?

In Newtonian gravitation, nowhere can you ever figure out

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I have to say, there is much of this I am not familiar with.

"the two is not exactly confirmed" Dark energy and General Relativity are pretty darn accurate. Are you suggesting that Dark energy could be something besides a constant? I don't know exactly what you mean here.

I am pretty confident that the theory of gravitational backreaction and dark energy being dynamical is just a way to save string theory, i.e. in compactified D brane cases. If not, I don't know exactly what you're talking about.

sorry for my ambigious statement.

GR is tested only in our solar system,and it's validity all over universe is not sure. Dark energy is confirmed,but Lamda CDM model is not!

that's the "two".

Yes, exactly,dark energy could be many many many things beside a cosmological constant.

yes,you don't know exactly what dynamical dark energy and gravitational backreaction is.

for the first, refer to "dynamics of dark energy" ,EJ Copeland, M Sami, S Tsujikawa - Arxiv preprint hep-th/0603057, 2006 ,

for the latter, search for brandenberger's papers on it.

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None of this makes sense to me. First, you never state if there is mass in your imaginary sphere, although I assume there is. Also, what mass is outside of this sphere?

In Newtonian gravitation, nowhere can you ever figure outwhytwo objects attract each other due to their mass. The force is assumed to be the hand of God. So, how does a sphere shrink? We know it does in Einstein's Relativity, because the space is drawn inward, but in Newtonian Gravitation, there is no explanation to justify that. You are just given that two masses will be attracted. This doesn't, in Newtonian Gravity, have any effect on the space itself, and therefore, the size of the sphere. The sphere would be unchanged in length, but the masses inside would attract.

sorry I'm non english native speaker.May be may presentation makes you confuse.

But what I'm talking about(the sphere thing) is typical textbook stuff.I would not explain textbooks here.

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We observe a constant acceleration, which is growing ever more dominate with distance. This is a constant acceleration, hence the cosmological constant.

just want to be sure, when you say acceleration you mean velocity right? i mean, the farther something is the faster it is (if at rest)?

- #17

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just want to be sure, when you say acceleration you mean velocity right? i mean, the farther something is the faster it is (if at rest)?

Be careful. When people talk about accelerated expansion they aren't talking about anything moving thru space.

It refers to the scalefactor a(t). Look up "Friedman equations" in Wiki. The scalefactor is a timevarying parameter that goes into computing spatial distances and it increases with time---governed by the Fr. eqns.

It doesn't say anything is moving. a(t) increasing simply means distances are increasing. That's to be expected---geometry is dynamic.

The current rate of increase is a'(t) and the rate of increase of the rate of increase is a"(t). You OK with Freshman calculus notation for first and second derivatives?

The Fr.eqns. show you how the first derivative and the second derivative of a(t) are determined. They are derived from the main Einstein eqn of GR, but represent a big simplification.

All that people mean by saying accelerated expansion is that the second deriv. of the scalefactor, namely a"(t), is positive. They're not talking about the Hubble law thing that larger distances increase at a higher rate (that's just a simple proportionality, not what is meant by acceleration.)

The reason why the rate of expansion a'(t) would be decreasing (except for the dark energy term Lambda) is obvious from looking at the first Friedman equation, the one that determines a"(t). It is clear that a" would be negative except for the Lambda term.

It is generally a bad idea to try to think about this in Newtonian terms----don't picture galaxies moving, having momentum, being slowed down by some force.

So Newtonian (motion-type) mechanics is a bad approach. What you need is Friedman mechanics Look at those equations, determining the evolution of a(t) the scalefactor. Instead of trying to think in terms of Newton's equations.

There is a phony derivation of Friedman model from Newtonian, but it is misleading: gives a false sense of comprehension. And makes people have trouble with the coordinate system that mainstream cosmology uses, and with the fact that distances typically increase faster than c, and (like you said) the approximate balance of gravity pull, and the idea of CMB rest---the Newton pseudo-explanation is rife with potential contradictions so it's better avoided.

Each galaxy (in avarage) doesn't "feel" gravity towards any specific direction so why should the expansion be slowing down due to gravity? even if the expansion is some sort of force, i don't see why it needs to use energy to overcome gravity, which is at balance...

This is good thinking!

Look at the second Fr. equation here

http://en.wikipedia.org/wiki/Friedmann_equations

The one that determines a"(t)/a(t), do you see it?

Do you see that it shows that a" must be negative unless there is a positive Lambda term?

Thats why (without Lambda) expansion rate would have to be declining---the answer to your thread title question.

And why are the equations trusted? Because they are derived from the Einstein eqn of GR, in the way the Wiki article says. And the GR equation is our theory of how geometry evolves. That is, our theory of how geometry/gravity behaves. It has been repeatedly tested and it is exquisitely precise. There isn't anything more basic than geometry, so there isn't anything more basic than GR.

Like, GR is the reason that the angles of a triangle add up to nearly 180 degrees (except for very small gravity effects that Euclid didn't know about.)

It is the reason that geometry is very nearly like what you learned in High School. GR is the reason why parallel lines almost never meet, and why Pythagoras. It is the reason for (approximate) flatness. And why the Earth presses on the soles of your feet.

It has passed all the experimental/observational tests so far and as soon as they find some discrepancy they will refine it and get GR version 1.1. But that hasn't happened yet. So for the time being we take it as right. (And Newton as not right).

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- #18

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it took me a while to realize that P isn't momentum :S but i think i managed to understand some of it :P (although i still don't see where it shows that a" must be negative unless there is a positive Lambda term)

i still don't get why (the favorite question) the gravity affects a".i mean, i can see how it is so by the equations but i don't understand the physics behind it. (like, you can explain why a ball jumps back from the floor by calculating momentum but to really understand you need to look at the forces and stuff :P)

- #19

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I hope I don't too much disturb marcus's educational efforts, but "understanding physics" quite often means "reducing to known concepts". In this case, I disagree with marcus about the usefulness of Newtonian mechanics: as long as you restrict yourself to a small patch of space (some hundred millions of lightyears, actually), the effect is quite accurately described by the gravitational influence of a homogeneous distribution of matter, where the density of DE is multiplied by -2, twice as repellant as ordinary matter would be attacting. Add "repellant matter" to your mental picture, use Newtonian mechanics, and you do fine in your neighbourhood.i still don't get why (the favorite question) the gravity affects a".i mean, i can see how it is so by the equations but i don't understand the physics behind it.

But keep in mind that it looks all the same in the neighbourhood of

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thank you very much!

it took me a while to realize that P isn't momentum :S but i think i managed to understand some of it :P (although i still don't see where it shows that a" must be negative unless there is a positive Lambda term)

...

Yes in that version of the equations, p is pressure associated with matter (not dark energy, as long as the Lambda term is there), and rho is the matter density. Matter pressure and density must be positive.

so if you put a minus sign in front of the rho and p term, it must be negative.

So the way they are writing it at first----the first two equations after giving the formula for the metric, the ratio a"/a is equal to a term which must be negative, plus the Lambda term.

That is why a" must be negative unless you have positive Lamda. Please ask again if you don't see this. I have explained it only very quickly and it may not be clear.

============================

Let's look again at the second Fr. eqn. sometimes called the

Just as a matter of taste I like to bring the c^2 out into the coefficient and interpret rho as an energy density. Remember now Lambda = 0.

a"/a = -(4piG/3c^2) (rho + 3p)

Since energy density and pressure have the same units, I like to write it this way because then

rho + 3p makes a nice package expressing the source of gravity (did you know that the pressure at the core of the sun contributes to its gravity?)

Anyway isn't it clear from this that a"/a is negative? If there is any matter in the universe at all!

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