Is a Cosmological Constant necessary to explain the Universe's expansion rate?

[Twistedseer]

How perception affect understanding

Taking a basic physics discovery, in this case “the Universe is expanding”.

Do you think that mankind existence in this relatively young stage of the Universe “colours” our perception of what we observe as expansion?

Does the static Universe have any validity?

Or can we perceive expansion, in a static Universe?

Twistedseer

 

[Chronos]

Mathematically, as Einstein discerned, the universe cannot be static. He added, mostly ad hoc, a cosmological constant to prevent the universe from collapsing. He later retracted that assertion. Right now, he is looking pretty smart again.

 

[Twistedseer]

Mathematically, as Einstein discerned, the universe cannot be static. He added, mostly ad hoc, a cosmological constant to prevent the universe from collapsing. He later retracted that assertion. Right now, he is looking pretty smart again.

Cannot be static, or is not currently static.

If you take the cosmological constant as the "force" that is currently preventing the universe from collapsing and currently forcing the universe to speed up its expansion... do you believe that it could be self-balencing.

Twistedseer

 

[Chronos]

I entirely agree it is self balancing and that it is a built in feature of the universe. Consider this:

Cosmologists have calculated that the critical density of the universe one billionth of a second after the BB was 4.47 x 10^23 grams per cubic centimeter. At that density, the universe is perfectly flat, causing it to eternally expand toward a certain limit, but never quite reaching that limit. Had the universe been only one gram/cc denser than 4.47 x 10^23 grams/cc, it was doomed to collapse and, in fact, we would already be in the Big Crunch phase (which we are not). On the other hand, if the universe was only one gram less than the critical density a billionth of a second after the big bang, it was destined to expand forever, and we would observe a universe that would not look like the one we reside in. So, the universe finds itself poised within 1 part in 447 sextillion between these three different fates:

If 1 part in 447 sextillion is not convincing enough, consider that if you calculate the critical density back to the Planck time limit [10E-43 seconds after the BB], the critical density limit is one part in 10^59 grams/cc. I don't mind coincidences, but that one is pretty hard to swallow. The only answer that makes any sense to me is that matter density [gravity] and the expansion force have been in perfect balance since the beginning of time. It also implies they are different manifestations of the same underlying force. My suspicion is that with further refinements in the detection of dark matter, etc., we will find that Omega is exactly equal to 1.0 and the universe is perfectly flat.

 

[Mike2]

The only answer that makes any sense to me is that matter density [gravity] and the expansion force have been in perfect balance since the beginning of time. It also implies they are different manifestations of the same underlying force. My suspicion is that with further refinements in the detection of dark matter, etc., we will find that Omega is exactly equal to 1.0 and the universe is perfectly flat.

When they say universe, what do they mean? If inflation only allows us to preceive only a fraction of the entire universe, then are they talking about the density within our current cosmological horizon? And if galaxies are disappearing behind that horizon, then how does that effect our observation of omega?

 

[Chronos]

When they say universe, what do they mean? If inflation only allows us to preceive only a fraction of the entire universe, then are they talking about the density within our current cosmological horizon?

Yes.

And if galaxies are disappearing behind that horizon, then how does that effect our observation of omega?

They can run, but not excape. Nothing within the our cosmological horizon can escape, just eventually become too faint to be seen. Bear in mind, the whole point of the inflation model is to account for the large scale homogenity of the observable universe. This necessitates a scenario where everything currently observable was at one time, however brief, within the same particle horizon. This occurred during the very early stages of the BB. This initial particle horizon permanently fixed the boundary of our cosmological horizon.

 

[Mike2]

Yes.They can run, but not excape. Nothing within the our cosmological horizon can escape, just eventually become too faint to be seen. Bear in mind, the whole point of the inflation model is to account for the large scale homogenity of the observable universe. This necessitates a scenario where everything currently observable was at one time, however brief, within the same particle horizon. This occurred during the very early stages of the BB. This initial particle horizon permanently fixed the boundary of our cosmological horizon.

Since thing approching the cosmological horizon start to "freeze", what do we precieve about their state of evergy and entropy? Would they lose kinetic energy since they no longer move? Is their a drop in entropy since they freeze? What does this mean for the energy content of the observable universe? What does it mean for the entire entropy state of the universe?

 

[Chronos]

It remains the same. Objects merely become increasingly redshifted as they approach [but never quite reach] the boundary.

 

[Garth]

How measurement might affect understanding

How perception affect understanding
Does the static Universe have any validity?

Some questions: In the normal expanding cosmological solution of General Relativity (GR) what exactly is expanding? If it is space-time itself, as demanded by the theory, then what expands with it? As the Schwarzschild solution for gravitational orbits is embedded in that space-time should not its solutions co-expand? Also as the Bohr/Schrödinger/Dirac equations of atomic physics are also so embedded then should not their solutions expand? If, as a consequence, gravitational orbits and atoms together with the physical rulers constructed of those atoms so co-expand with the universe, then surely there would be no detectable expansion? Therefore if cosmological red shift is not caused by recession it might instead be caused by the secular increase of the inertial mass of the measuring apparatus and all fundamental particles.
The static universe?

Just a thought.

- Garth

 

[Mike2]

Some questions: In the normal expanding cosmological solution of General Relativity (GR) what exactly is expanding? If it is space-time itself, as demanded by the theory, then what expands with it? As the Schwarzschild solution for gravitational orbits is embedded in that space-time should not its solutions co-expand? Also as the Bohr/Schrödinger/Dirac equations of atomic physics are also so embedded then should not their solutions expand? If, as a consequence, gravitational orbits and atoms together with the physical rulers constructed of those atoms so co-expand with the universe, then surely there would be no detectable expansion? Therefore if cosmological red shift is not caused by recession it might be caused by the secular increase of the inertial mass of the measuring apparatus and all fundamental particles.
The static universe?

Just a thought.

- Garth

IIRC, it is the cosmological constant that is supposed to be responsible for the expansion of the universe. Normal matter gives rise to the stress-energy tensor. But then when we add the CC term, the curvature of the universe changes resulting in space itself expanding.

 

[Garth]

IIRC, it is the cosmological constant that is supposed to be responsible for the expansion of the universe. Normal matter gives rise to the stress-energy tensor. But then when we add the CC term, the curvature of the universe changes resulting in space itself expanding.

I'm afraid that that is not a correct understanding of standard GR.

The universe described by the Friedmann-Robertson-Walker metric expands, or contracts, as an inevitable feature of space-time without the cosmological constant. The FRW metric is the cosmological solution to Einstein's field equation. Indeed Einstein introduced the CC (a type of integration constant) in order to stop the universe expanding, he wanted a static one for philosophical reasons. However his model would be unstable. Recently the CC has been re-introduced to explain Dark Energy and cosmological acceleration, which is different to standard expansion, and some models require a varying cosmological constant - and if that is not a contradiction in terms I don't know what is!

The discovery of Hubble red shift immediately confirmed cosmological expansion, however from my post above you may realize that I'm not so sure! GR may require modification (to integrate it with quantum cosmology?) and Hubble red shift may have another interpretation.

Garth

 

[Mike2]

I'm afraid that that is not a correct understanding of standard GR.

The universe described by the Friedmann-Robertson-Walker metric expands, or contracts, as an inevitable feature of space-time without the cosmological constant. The FRW metric is the cosmological solution to Einstein's field equation. Indeed Einstein introduced the CC (a type of integration constant) in order to stop the universe expanding, he wanted a static one for philosophical reasons. However his model would be unstable. Recently the CC has been re-introduced to explain Dark Energy and cosmological acceleration, which is different to standard expansion, and some models require a varying cosmological constant - and if that is not a contradiction in terms I don't know what is!

The discovery of Hubble red shift immediately confirmed cosmological expansion, however from my post above you may realize that I'm not so sure! GR may require modification (to integrate it with quantum cosmology?) and Hubble red shift may have another interpretation.

Garth

Again, as I recall, and I am no expert, the radius of expansion seems to be put into the metric by hand simply to explain expansion/contraction. Put I seem to have missed what mechanisms give rise to the scale factor.

Let's see, given the metric (with its scale factor) one can come up with the the stress-energy tensor. But I don't remember what components of the tensor are responsible for the scale factor changing. I suppose it would not be normal matter in the tensor that would change. So it must be some other part.

I've recently read, "Relativity", by Hans Stephani. It's an introduction; you get to see the equations and he explains what the variables mean. But that's about it. His derivations are sketchy at best. Do you know of any better modern books on relativity that takes more care to explain things? Thanks.

 

[geometer]

I've recently read, "Relativity", by Hans Stephani. It's an introduction; you get to see the equations and he explains what the variables mean. But that's about it. His derivations are sketchy at best. Do you know of any better modern books on relativity that takes more care to explain things? Thanks.

My favorite is "A first course in general relativity," by Bernard F. Schutz. It's an excellent introduction to general relativity. It assumes you have a basic familiarity with special relativity, vector calculus, ordinary and simple partial differential equations.

 

[Garth]

Try "Introducing Einstein's Relativity" Ray d'Inverno,
or the classic texts "Gravitation and Cosmology" Weinberg,
"Gravitation" Misner, Thorne and Wheeler (you''ll need strong arms to carry it home!)
"General Relativity" R Wald.

Garth

 

[Chronos]

...Einstein introduced the CC (a type of integration constant) in order to stop the universe expanding, he wanted a static one for philosophical reasons

A minor correction, if I may. Einstein added the CC to prevent the universe from collapsing...

Einstein initially included the term because he was dissatisfied by the fact that his equations would not allow for a static universe. Gravity would cause a universe which was initially at rest to begin to contract. To counteract the force of gravity, Einstein added the cosmological constant which would produce a repulsive force.
[Wikipedia]

 

[Garth]

A minor correction, if I may. Einstein added the CC to prevent the universe from collapsing...

Thank you - it is important to get these things right!
Garth

Why keep silent for fear of making a fool of yourself when you can speak and prove that you are?

 

[Mike2]

I'm afraid that that is not a correct understanding of standard GR.

The universe described by the Friedmann-Robertson-Walker metric expands, or contracts, as an inevitable feature of space-time without the cosmological constant. The FRW metric is the cosmological solution to Einstein's field equation. Indeed Einstein introduced the CC (a type of integration constant) in order to stop the universe expanding, he wanted a static one for philosophical reasons. However his model would be unstable. Recently the CC has been re-introduced to explain Dark Energy and cosmological acceleration, which is different to standard expansion, and some models require a varying cosmological constant - and if that is not a contradiction in terms I don't know what is!

Let's see... without a CC, the universe can only decelerate its expansion. It may continue to expand forever, but at an ever slower rate. So isn't a CC needed to get even a constant expansion rate, neither accelerating nor decelerating?

 

[Garth]

Let's see... without a CC, the universe can only decelerate its expansion. It may continue to expand forever, but at an ever slower rate. So isn't a CC needed to get even a constant expansion rate, neither accelerating nor decelerating?

The first half is correct, however a CC would not keep the expansion rate constant, it can halt it completely if balanced exactly right, which is what Einstein used it for, but his static universe would have been unstable. In GR the only way to get a linearly expanding or "freely coasting" model
R = ct
would be if the density were zero and curvature were hyperbolic (k = -1), this is Milne's empty universe.

In fact in the standard model a CC, or Dark Energy, or 'quintessence', or leakage from a higher dimension/other brane or etc. etc. are required to explain the observation of the fainter-than-expected distant Type Ia Supernovae, which is normally interpreted as an acceleration of the universe's expansion.

Garth