Cosmological Constant

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rod

Oct 22, 2019
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Helio, the calculation for the CC and vacuum energy density is done to match the CMBR today, not predict it. Einstein CC in GR originally was never used like this and the CC value was modified later to show the expanding universe vs. a CC value that showed GR calculated a static universe. The modification to the CC allowed the expanding universe but a universe only about 2 billion years old with H0 about 500 km/s/Mpc and no CMBR known until the work of George Gamow and Ralph Alpher, but a very different CMBR than what is observed today these folks predicted, clearly this CMBR constraint for CC is not the same as the modern CMBR constraints for CC you referenced. Thus in my view, CC remains a free parameter, adjusted as cosmology needs arise. You do not need to agree with me, but this is how I see it. Modern BB cosmology today goes back beyond 1 second after BB (t < second back to beginning or at least the Plank time and Planck length), thus we enter the realm of the quantum universe for origins teaching today and exotic new physics, particles, and vacuum energy changes :) Perhaps a good chart showing all these changes, CC, vacuum energy density changes, etc. from Planck time until BBN ended, could be interesting to study :)

And I will add, from BBN ending until CMBR formed.
 
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Jun 1, 2020
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Helio, the calculation for the CC and vacuum energy density is done to match the CMBR today, not predict it.
Right. The BBT predicts that a known blackbody radiation profile at about 3000K when Recombination took place has redshifted to about 2.73K. The theory doesn't predict an actual value no more than a theory of steel will predict the yield strength of a certain alloy. But what is observed by testing will give us that value. But if you want to call it a free parameter, then you could still be right, I suppose.


Einstein CC in GR originally was never used like this and the CC value was modified later to show the expanding universe vs. a CC value that showed GR calculated a static universe.
No. The original GR work didn't take all of the cosmos into account since Einstein falsely, like everyone else in his day, that the universe was static. It was never used to calculate a static one.

Modern BB cosmology today goes back beyond 1 second after BB (t < second back to beginning or at least the Plank time and Planck length), thus we enter the realm of the quantum universe for origins teaching today and exotic new physics, particles, and vacuum energy changes :) Perhaps a good chart showing all these changes, CC, vacuum energy density changes, etc. from Planck time until BBN ended, could be interesting to study :)

And I will add, from BBN ending until CMBR formed.
Indeed. :)
 
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rod

Oct 22, 2019
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Helio, be careful here. "No. The original GR work didn't take all of the cosmos into account since Einstein falsely, like everyone else in his day, that the universe was static. It was never used to calculate a static one."

My answer, yes the CC was used to calculate a static universe using GR equations. https://phys.org/news/2014-02-einstein-conversion-static-universe.html

"In 1917 Einstein applied his theory of general relativity in the universe, and suggested a model of a homogenous, static, spatially curved universe. However, this interpretation has one major problem: If gravitation was the only active force, his universe would collapse – an issue Einstein addressed by introducing the cosmological constant. He then fiercely resisted the view that the universe was expanding, despite his contemporaries' suggestions that this was the case. "

There is more to the story about the origins of CC it seems :) It seems lambda was used to create a universe (much smaller than the universe claimed today in BB cosmology) that prevented gravity from collapsing the universe and allowed a static universe to exist as well. Adjusting CC can change everything it seems.


"Abstract
In 1917 Einstein initiated modern cosmology by postulating, based on general relativity, a homogenous, static, spatially curved universe. To counteract gravitational contraction he introduced the cosmological constant. In 1922 Alexander Friedman showed that Albert Einstein’s fundamental equations also allow dynamical worlds, and in 1927 Georges Lemaître, backed by observational evidence, concluded that our universe was expanding. Einstein impetuously rejected Friedman’s as well as Lemaître’s findings. However, in 1931 he retracted his former static model in favour of a dynamic solution. This investigation follows Einstein on his hesitating path from a static to the expanding universe. Contrary to an often advocated belief the primary motive for his switch was not observational evidence, but the realisation that his static model was unstable."
 
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My answer, yes the CC was used to calculate a static universe using GR equations. https://phys.org/news/2014-02-einstein-conversion-static-universe.html
That article doesn't demonstrate that a static universe comes out of the GR equations. It is clear that Einstein's well-known, and popular, conviction for a static universe was why the a CC was not considered.

The end of that article is puzzling by suggesting they finally developed, along with de Sitter, an expanding universe but with no expansion constant. That seems absurd. How can you expand with a zero expansion rate? I suspect they may be referring to the time both these physicists had their zero expansion models. The article makes it sound as if Einstein woke up with the Lemaitre model and then produced a superior one, as well as de Sitter. I'm not sure that is what happened. Many GR cosmological models came forth after Lemaitre, but BBT isn't also known as the Einstein model, so I suspect the article is either misleading or wrong in their last paragraph.


"In 1917 Einstein applied his theory of general relativity in the universe, and suggested a model of a homogenous, static, spatially curved universe. However, this interpretation has one major problem: If gravitation was the only active force, his universe would collapse – an issue Einstein addressed by introducing the cosmological constant. He then fiercely resisted the view that the universe was expanding, despite his contemporaries' suggestions that this was the case. "
Right, notice they aren't saying that a static universe is a requirement for GR, but that Einstein "suggested a ... static... unvierse". IOW, his GR work only assumed a static universe.

There is more to the story about the origins of CC it seems :) It seems lambda was used to create a universe (much smaller than the universe claimed today in BB cosmology) that prevented gravity from collapsing the universe and allowed a static universe to exist as well.
Yes. He may have been using the early calculations that were derived from Hubble's very fast expansion rate due to his Cepheid error, that was only discovered after Pop II stars were realized. Hubble's work revealed a CC of about 500 kps/Mpc, IIRC. So the universe would have been only about 2Gyrs old, though some rocks were being found to have ages older than 3 Gyrs, and some stars were found to be older as well. Having a universe younger than rocks and stars was strong objective evidence something was a wrong. :) The weakest element was clearly with Hubble since it isn't hard to imagine that those measurements were still immature within the astronomy world. Of course, that's what actually happened.

It wasn't hard to predict back then that the CC would take a lot of effort to determine with some degree of accuracy. Lemaitre seems to be first to recognize this when he did his crude calculation. But it was Lemaitre that argued for an expansion. Something Hubble never did, yet it is called the Hubble Constant. :)
 
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rod

Oct 22, 2019
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Helio, in your post #29, keep your eye on the bouncing CC :)

https://ui.adsabs.harvard.edu/abs/2020arXiv200813501O/abstract, and arxiv paper, https://arxiv.org/ftp/arxiv/papers/2008/2008.13501.pdf

An interesting 27 page report to read.

"By contrast, Einstein and de Sitter constructed a specific cosmic model with both spatial curvature and the cosmological constant set to zero with the express purpose of establishing a simple relation between the rate of expansion and the mean density of matter that could be compared with observation." "4.2 On the rate of expansion and the density of matter. As noted above, setting both spatial curvature and the cosmological constant to zero in their model enabled the authors to derive a simple relation between the rate of expansion and the mean density of matter that could be tested against observation. Thus, taking Hubble’s redshift/distance value of 500 km s^-1 Mpc^-1 for the fractional rate of expansion, they derived a value of 4x10^-28 g/cm3 for the density of matter."

"The Einstein-de Sitter model became very well-known and went on to play a significant role
in 20th century cosmology...Assuming a vanishing cosmological constant, a cosmos of mass density higher than
the critical value would be of closed spatial geometry and eventually collapse, while a cosmos
of mass density less than the critical value would be of open spatial geometry and expand at an
ever increasing rate; in between lay the critical case of a cosmos with Euclidean geometry that
would expand at an ever decreasing rate."

"While today’s Ʌ-CDM model of a cosmos of Euclidean geometry with a positive cosmological constant is a much better fit to current observational data, the physical meaning of dark energy remains elusive."

I see a *bouncing* CC in cosmology :)
 
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Thanks. That shows that the joint 1932 work of Einstein and de Sitter was influential. [This is after they recognized Lemaitre's work and not their troubled original and separate work.] This work was based on Hubble's erroneous data giving a 2Gyr universe, but the importance of a critical density model carried a lot of weight.

I am confident mainstream cosmology, as they note in the paper, favors that Lambda-CDM model, hence the extensive efforts to refine the CC.

"While today’s Ʌ-CDM model of a cosmos of Euclidean geometry with a positive cosmological constant is a much better fit to current observational data, the physical meaning of dark energy remains elusive."
Right. DE is a contrived term to describe an effect without any clear idea as to the cause, though there are several dozen theories, IIRC.

I see a *bouncing* CC in cosmology :)
True, but the bouncing today is very tiny. There aren't many "constants" used in cosmology that don't have at least a little bounce. :) Partly because they aren't independent from one another.
 
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