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 pivoxa15 Dec16-05 09:57 PM

cosmological constant?

Einstein introduced the cosmological constant to keep a static universe

But we know the universe is expanding due to dark matter?

The exstistence of dark matter promotes the cosmoloigcal constant again.

How does that make sense?

Static universe: need cosmological constant
Expanding universe with dark matter: need cosmological constant

Or is it the case of adding the constant and the latter case minusing the constant

 dicerandom Dec16-05 10:35 PM

It's a matter of the size of the cosmological constant. The constant's actually always been there, it's a part of the general form of solutions to Einstein's Field Equations, however it was chosen to be zero to match observations at the time. There has been talk recently of re-introducing it, I believe I read something recently where some researchers found a value that matched observed expansion to within 10%.

 Garth Dec17-05 03:17 AM

Quote:
 Quote by pivoxa15 The exstistence of dark matter promotes the cosmoloigcal constant again. How does that make sense?
No - it is Dark Energy that may be identified as the cosmological constant.
Quote:
 Static universe: need cosmological constant Expanding universe with dark matter: need cosmological constant Or is it the case of adding the constant and the latter case minusing the constant
It is the accelerating universe that needs a cosmological constant.

Counter-intuitively adding pressure to the universe increases the deceleration of its expansion rate. This is because pressure adds a form of energy and energy is equivalent to mass that adds gravitation. It is the self gravitation of the mass-energy within the universe that should cause its expansion to decelerate.

The cosmological constant may be interpreted as a form of negative pressure, which Einstein originally used to counter this self-attraction. He wanted to prevent the universe either expanding or collapsing to yield a static universe, the CC balanced the gravitational forces on a large scale within the universe.

When observations of distant Type Ia super novae were interpreted to indicate that the unverse was actually accelerating, not decelerating as previously expected, then a negative pressure was invoked to deliver this.
The negative pressure is a property of something called Dark Energy, and about 73% of the universe's mass is required to be in this form to make the standard LCDM model work. It is anybody's guess as to what Dark Energy actually is and something can be learned from the equation of state it must have to 'save the appearances' of that model.

The simplest suggestion and the one with an equation of state that seems to work ($p = -\rho c^2$) is the Cosmological Constant.

I hope this helps,

Garth

 pivoxa15 Dec17-05 10:05 PM

The cosmological constant may be interpreted as a form of negative pressure, which Einstein originally used to counter this self-attraction. He wanted to prevent the universe either expanding or collapsing to yield a static universe, the CC balanced the gravitational forces on a large scale within the universe.

So the negative pressure which is the CC will yield a static universe?

When observations of distant Type Ia super novae were interpreted to indicate that the unverse was actually accelerating, not decelerating as previously expected, then a negative pressure was invoked to deliver this.

So the negative pressure which is the CC will yield an accelerating expanding universe?

How can an equation containing one particular (in this case negative pressure in both cases) constant yield two solutions that contradict each other? That is a static universe and an acclerating expanding universe.

 dicerandom Dec17-05 10:38 PM

Quote:
 Quote by pivoxa15 How can an equation containing one particular (in this case negative pressure in both cases) constant yield two solutions that contradict each other? That is a static universe and an acclerating expanding universe.
The cosmological constant is a multiplicitive factor in front of a term which has the effect of a negative pressure. If you choose the value of that constant to be one number you get Einstein's static universe, if you choose it to be another number you get the accelerating expansion case.

 Janus Dec18-05 01:31 PM

Quote:
 Quote by pivoxa15 The cosmological constant may be interpreted as a form of negative pressure, which Einstein originally used to counter this self-attraction. He wanted to prevent the universe either expanding or collapsing to yield a static universe, the CC balanced the gravitational forces on a large scale within the universe. So the negative pressure which is the CC will yield a static universe? When observations of distant Type Ia super novae were interpreted to indicate that the unverse was actually accelerating, not decelerating as previously expected, then a negative pressure was invoked to deliver this. So the negative pressure which is the CC will yield an accelerating expanding universe? How can an equation containing one particular (in this case negative pressure in both cases) constant yield two solutions that contradict each other? That is a static universe and an acclerating expanding universe.
In the first case, the CC is finely tuned such that it exactly balances the gravitational attaction. This actually turned out to be a problem because unless the CC had exactly the right value, it would lead to either a colapse or run away expansion of the universe.

When it was discovered that the universe was expanding rather than static, the whole CC term was put aside as it really was no longer needed. (the expansion could be explained as the lingering effect of the impetus of the Big Bang)

If this were the case, then we would expect the expansion rate to slow over time. The supernovae observations mentioned were an attempt to determine whether this slowing was enough to ever stop the expansion completely, or if the universe would keep on expanding forever.

The results indicated, as already mentioned, that the expansion rate was actually speeding up. IOW, it appeared to be undergoing the run away expansion suggested if the CC had too large a value.

Simply put:

For a static universe the negative pressure has to have a precise value in order to perfectly balance the gravitational attraction of the universe.

If it is too small, the universe collapses
If it is too large, the universe expands at an accelerating rate.

If the universe is expanding simply due to the impetus of the Big bang,(no CC) the expansion will decelerate with time.

Due to changes in our understanding of the universe through improved observations, the expected value of the CC has had to change.

 Chronos Dec19-05 12:18 AM

The problem is, as Einstein realized, the universe cannot remain perfectly poised between collapse and expansion indefinitely. Small, local fluctuations in density [such as galaxies] would eventually tip the balance in one or the other direction.

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