Rate of universe expansion question

[AdamLin]

To my knowledge gravity acts like a brake for expansion. The force of gravity depends on the amount of mass that an object has. On a large scale, mass in the universe is evenly distributed. Is the distribution of mass completely even or is it mostly even? Would different parts of the universe expand at different rates because of their mass differences? Thanks

 

[Drakkith]

Ok, I think I can answer this:

The strength of gravity is enough to counteract expansion only at the scale of galaxy clusters (or super clusters) and smaller. (IE galaxy clusters, galaxies, star systems, etc)

Once you get into scales above this we see that the universe is expanding. So, different parts of the universe do in fact expand differently, as some parts are nearer or further from gravitational sources. However, the effect smooths out on the large scales and results in an "average" expansion for the whole universe.

Someone correct me if that is incorrect.

 

[renjith_p]

If the universe were expanding and its accelerating at a rate of, say 'X' m/sec square. Then, does it mean that, all the matter in the universe is gaining some velocity each instant?
If so, on examining Einstein's equation, E=mc², it tells us that, if matter could be brought to the speed of light squared, it would no longer be matter but energy.
Is it possible that, one day, all the matter in the universe would reach that speed and and turn to energy?

 

[clamtrox]

If the universe were expanding and its accelerating at a rate of, say 'X' m/sec square. Then, does it mean that, all the matter in the universe is gaining some velocity each instant?
If so, on examining Einstein's equation, E=mc², it tells us that, if matter could be brought to the speed of light squared, it would no longer be matter but energy.
Is it possible that, one day, all the matter in the universe would reach that speed and and turn to energy?

No, that's not true at all.

In short, I only care about velocities in general relativity if the thing that's moving is right next to me. When it's in the other side of our observable universe, I could not care less. This is because the velocity I measure has no physical meaning; only local measurements do.

 

[clamtrox]

Ok, I think I can answer this:

The strength of gravity is enough to counteract expansion only at the scale of galaxy clusters (or super clusters) and smaller. (IE galaxy clusters, galaxies, star systems, etc)

Once you get into scales above this we see that the universe is expanding. So, different parts of the universe do in fact expand differently, as some parts are nearer or further from gravitational sources. However, the effect smooths out on the large scales and results in an "average" expansion for the whole universe.

Someone correct me if that is incorrect.

The problem is though, that the expansion of an averaged universe does not need to be same as the average expansion. To put that in mathematical terms,
$\langle G_{\mu \nu}(g_{\mu \nu}) \rangle \neq G_{\mu \nu} (\langle g_{\mu \nu}\rangle)$
because Einstein tensor depends nonlinearly on the metric.

 

[Drakkith]

If the universe were expanding and its accelerating at a rate of, say 'X' m/sec square. Then, does it mean that, all the matter in the universe is gaining some velocity each instant?

Recession velocity yes, but this is not the same as velocity as you would measure a car moving past you. It is due to the expansion of space and not local motion.

If so, on examining Einstein's equation, E=mc², it tells us that, if matter could be brought to the speed of light squared, it would no longer be matter but energy.

No, this is not what the equation means at all. First, nothing with mass can ever reach the speed of light. Second, what the equation tells us is that, given the right processes, an amount of mass can be converted into an amount of energy. The M is for Mass, not matter.

Is it possible that, one day, all the matter in the universe would reach that speed and and turn to energy?

No.

 

[Drakkith]

The problem is though, that the expansion of an averaged universe does not need to be same as the average expansion. To put that in mathematical terms,
$\langle G_{\mu \nu}(g_{\mu \nu}) \rangle \neq G_{\mu \nu} (\langle g_{\mu \nu}\rangle)$
because Einstein tensor depends nonlinearly on the metric.

I'll have to take your word for it, as the math eludes me.

 

[renjith_p]

Ok. Thankyou.

 

[Naty1]

To my knowledge gravity acts like a brake for expansion.

I'm going to take the opposite view and say, 'no' that's 'backwards! :

Cosmological expansion is CAUSED by gravity, specifically by the negative pressure, sometimes called the cosmological constant, of the vacuum of spacetime. So gravity causes the expansion of space. In fact, as new space it 'born' it arrives with it's own [constant] cosmological constant causing further expansion...it comes with the same dark energy density as 'old' space...it is not just new 'empty space' but new space with more negative pressure. Guess what: that causes an acceleration of expansion and energy dominates matter more and more as the universe evolves. Matter domination gives way to energy domination.

let's see if I can support that claim [from my notes] :

...The findings offer new support for the favored theory [meaning Einstein's general theory] of how dark energy works -- as a constant force, uniformly affecting the universe and propelling its runaway expansion... "The results tell us that dark energy is a cosmological constant, as Einstein proposed. If [regular,typical] gravity were the culprit, then we wouldn't be seeing these constant effects of dark energy throughout time."

[sorry, don't have that source.]

The cosmological constant has negative pressure equal to its energy density and so causes the expansion of the universe to accelerate... A major outstanding problem is that most quantum field theories predict a huge cosmological constant from the energy of the quantum vacuum, more than 100 orders of magnitude too large.

http://en.wikipedia.org/wiki/Dark_en...ative_pressure

According to General Relativity, the [positive] pressure within a substance contributes to its gravitational attraction for other things just as its mass density does. ...
[negative pressure is repulsive]

[no source]

same idea, from a previous post of mine:

The idea is that negative pressure could produce antigravity, and negative pressure means that something acquires energy when it expands. Virtual particles in vacuum would do that—an expanding vacuum just gives you more vacuum, so if the virtual particles have some "dark" energy associated with them, then more vacuum means more energy via negative pressure. Voila, antigravity.

and a slightly different perspective...but only slightly...

...The Lambda-Cold Dark Matter (LCDM) model, which is today the standard model in cosmology, assumes the presence of the cosmological term in the Einstein's equations...
In gravitational physics there is nothing 'mysterious' in the cosmological constant. At least nothing more mysterious than the Maxwell equations, the Yang-Mills equations, the Dirac equation, or the Standard Model equations. These equations contain constants whose values we are not able to compute from first principles. The cosmological constant is in no sense more of a "mystery" than any other among the numerous constants in our fundamental theories...

http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.3966v2.pdf

 

[Naty1]

On a large scale, mass in the universe is evenly distributed. Is the distribution of mass completely even or is it mostly even? Would different parts of the universe expand at different rates because of their mass differences?

A brief answer is the observed Hubble expansion is as far as is known the same in all directions. So the universe is expanding uniformly in all directions to the experimental accuracy we can measure. Another roughly equivalent way to say this is that we believe that over large distances space is essentially flat...without much curvature...without much gravity.

 

[marcus]

I'm going to take the opposite view and say, 'no' that's 'backwards! :

Cosmological expansion is CAUSED by gravity, specifically by the negative pressure, sometimes called the cosmological constant, of the vacuum of spacetime.

But Naty, until 1998 we thought the cosmo constant was zero. So it can hardly be the sole cause.
We still think that for the first few billion years its contribution was negligible. I think you know this well but it doesn't come thru.
Expansion is a solution to the basic equation with zero cosmo const.
So it seems strange to say expansion is CAUSED by it. It gives the impression that it is the MAIN cause, which is not the case. So far it makes a minor or secondary contribution, just a bit of gradual acceleration added on to the basic expansion. I think you thoroughly understand this, but it doesn't come across that way in the post.

BTW I see you quoted the Bianchi Rovelli article http://arxiv.org/abs/1002.3966 which I think is great! Their view is that it's just a constant, like Newton's G, that occurs naturally in the GR equation. Not a "dark energy" or "negative pressure". Not to be confused with the "vacuum energy" of quantum field theory---a theory which is worked out on the fixed non-expanding Minkowski space of 1905 special relativity. It's a very sensible viewpoint to take, I think. Glad you cited it! Folks should take a look at the whole article, which is short and mostly non-technical.