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I was reading this article, https://earthsky.org/space/this-date-in-science-edwin-hubble-and-the-expanding-universe . Please note that my understanding is very basic. You could find my main question toward the end. I have commented on excerpts from different sources below so that you're in a better position to understand where I'm going wrong and how I'm interpreting it. I hope it'd make it easier for you to help me. Thank you.

The following quote is taken from the mentioned article. I've boldfaced the part which originally confused and led me to post my question.

It’s said that Albert Einstein was elated to hear of Hubble’s work. Einstein’s Theory of Relativity implied that the universe must either be expanding or contracting. But Einstein himself rejected this notion in favor of the accepted idea that the universe was stationary and had always existed. When Hubble presented his evidence of the expansion of the universe, Einstein embraced the idea. He called his adherence to the old idea “my greatest blunder.”

I don't think that the original theory of general relativity implied expanding universe as is said above. I'd say that Einstein introduced cosmological constant as a way to counteract gravity so that the universe doesn't ultimately collapses onto itself. The three excerpts below seem to support my view.

Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow, apparently, for a static universe: gravity would cause a universe that was initially at dynamic equilibrium to contract. To counteract this possibility, Einstein added the cosmological constant.[3] However, soon after Einstein developed his static theory, observations by Edwin Hubble indicated that the universe appears to be expanding; this was consistent with a cosmological solution to the original general relativity equations that had been found by the mathematician Friedmann, working on the Einstein equations of general relativity. Einstein reportedly referred to his failure to accept the validation of his equations—when they had predicted the expansion of the universe in theory, before it was demonstrated in observation of the cosmological redshift— as his "biggest blunder".[10]

In fact, adding the cosmological constant to Einstein's equations does not lead to a static universe at equilibrium because the equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe that contracts slightly will continue contracting.[11]

Source 1: https://en.wikipedia.org/wiki/Cosmological_constant#History

The cosmological constant was first proposed by Einstein as a mechanism to obtain a solution of the gravitational field equation that would lead to a static universe, effectively using dark energy to balance gravity.[16] Einstein gave the cosmological constant the symbol Λ (capital lambda)....

The mechanism was an example of fine-tuning, and it was later realized that Einstein's static universe would not be stable: local inhomogeneities would ultimately lead to either the runaway expansion or contraction of the universe. The equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe which contracts slightly will continue contracting. These sorts of disturbances are inevitable, due to the uneven distribution of matter throughout the universe. Further, observations made by Edwin Hubble in 1929 showed that the universe appears to be expanding and not static at all. Einstein reportedly referred to his failure to predict the idea of a dynamic universe, in contrast to a static universe, as his greatest blunder.[19]

Source 2: https://en.wikipedia.org/wiki/Dark_energy#History_of_discovery_and_previous_speculation

In 1912, Vesto Slipher discovered that light from remote galaxies was redshifted,[8][9] which was later interpreted as galaxies receding from the Earth. In 1922, Alexander Friedmann used Einstein field equations to provide theoretical evidence that the universe is expanding.[10] In 1927, Georges Lemaître independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented the first observational evidence for a linear relationship between distance to galaxies and their recessional velocity.[11] Edwin Hubble observationally confirmed Lemaître's findings two years later.[12] Assuming the cosmological principle, these findings would imply that all galaxies are moving away from each other.

Based on large quantities of experimental observation and theoretical work, the scientific consensus is that space itself is expanding, and that it expanded very rapidly within the first fraction of a second after the Big Bang. This kind of expansion is known as "metric expansion". In mathematics and physics, a "metric" means a measure of distance, and the term implies that the sense of distance within the universe is itself changing.

Source 3: https://en.wikipedia.org/wiki/Expansion_of_the_universe#History

Further, I don't think it was a blunder on Einstein's part to remove the constant, as is stated in the excerpt below from Source 4. Einstein had used the cosmological constant to balance the attractive force gravity so that the end result was static universe as the static model was preferred at that time. It's not that if Einstein hadn't removed the constant, it'd have resulted into expanding universe. In my opinion, removing it would have rather resulted into collapsing universe which Einstein had initially tried to prevent.

Albert Einstein invented the cosmological constant as part of his theory of gravity, known as General Relativity.

Einstein’s equations showed that the gravity of all the matter in the universe would exert a strong pull, pulling all the stars and galaxies toward each other and eventually causing the universe to collapse. At the time, though, astronomers believed that the universe was static – that it was neither expanding nor contracting. To counteract this problem, Einstein added another term to his equations, called the cosmological constant, to balance the inward pull of gravity.

Within about a decade, though, astronomer Edwin Hubble discovered that the universe is expanding. Einstein discarded the cosmological constant, calling it his greatest scientific blunder.

When dark energy was discovered, though, many physicists began to think that Einstein’s only blunder was in removing the constant. This "repulsive" force could begin to explain the acceleration of the universe. In other words, it might be the dark energy.

Source 4: http://hetdex.org/dark_energy/what_is_it/vacuum_energy.html

MAIN QUESTION:

Dark energy was discovered in the 1990 as stated in Source 6 and I also think, as in Source 5, that dark energy is quite different from the cosmological constant. Around 1930 Einstein was convinced that the universe was expanding, did he entirely remove the constant from his equations or did he change its value so that the equations predict expanding universe? What was thought at that time as the cause of expansion? What was there in the space which was pushing it apart? How did Friedmann in 1922 reach the conclusion that the universe was expanding using the original equations of general relativity laid down by Einstein? What was Friedmann's motivation? I found a similar question here but the answer is mathematical heavy and I couldn't make any sense of it at all.

Basilakos and Sola instead suggest that dark energy is a type of dynamic quantum vacuum energy — something different than Einstein's cosmological constant, which describes a static vacuum energy density and is another possible explanation of dark energy's nature.

Source 5: https://www.space.com/25238-dark-energy-quantum-vacuum-theory.html

Dark energy is even more mysterious, and its discovery in the 1990s was a complete shock to scientists. Previously, physicists had assumed that the attractive force of gravity would slow down the expansion of the universe over time. But when two independent teams tried to measure the rate of deceleration, they found that the expansion was actually speeding up. One scientist likened the finding to throwing a set of keys up in the air expecting them to fall back down-only to see them fly straight up toward the ceiling.

Source 6: https://www.nationalgeographic.com/science/space/dark-matter/

It has become a popular belief that Albert Einstein abandoned his static universe when, on a visit to Pasadena in January and February 1931, Edwin Hubble showed him the redshifted nebular spectra and convinced him that the universe was expanding, and the cosmological constant was superfluous.

Source 7: https://arxiv.org/ftp/arxiv/papers/1311/1311.2763.pdf (Einstein’s conversion from his static to an expanding universe)

Helpful links:

1: What's the difference between "dark energy" and "vacuum energy"?

2: https://www.youtube.com/watch?v=g20JZ2HNZaw

EDIT #1: (added on 12-25-2020, 12:26 PM UTC)

Earlier at the beginning on this post I said, "I don't think that the original theory of general relativity implied expanding universe as is said above. I'd say that Einstein introduced cosmological constant as a way to counteract gravity so that the universe doesn't ultimately collapses onto itself."

I think I should add more to it. I was watching the documentary "The Fabric of the Cosmos: What Is Space?" presented by Brian Greene.

The following is said around 40:33 - 43:10.

and the discovery of dark energy held another surprise the idea that the universe contains such an ingredient had actually been cooked up eighty years earlier I'll let you in on a little secret although he didn't call it dark energy long ago Albert Einstein predicted that space itself could exert a force that would drive galaxies apart you see shortly after discovering his general theory of relativity his theory of gravity Einstein found that according to the mathematics the universe would either be expanding or contracting but it couldn't hover at a fixed size this was puzzling because before they knew about the Big Bang most scientists including Einstein pictured the universe as static eternal and unchanging when Einstein's equations suggested an expanding or contracting universe not the static universe everyone believed in he had a problem so Einstein went back to his equations and modified them to allow for kind of anti-gravity that would infuse space with an outward push counteracting usual inward pull of gravity allowing the universe to stand still he called the modification the cosmological constant adding the cosmological constant rescued his equations but the truth is Einstein had no idea if his outward push or anti-gravity really existed the introduction of the cosmological constant by Einstein was not a very elegant solution to try to find what he was looking for stationary universe it achieves this effect of anti-gravity it says that gravity sometimes can behave in such a way is not to pull things together but to push things apart like the clash of two titans the cosmological constant and the pull of ordinary matter could hold the universe in check and keep it static but about a dozen years later the astronomer Edwin Hubble discovered the universe is not static it's expanding due to the explosive force of the Big Bang fourteen billion years ago that meant Einsteins original equations no longer had to be altered so suddenly the need for a cosmological constant went right out the window.

It's understandable that the gravity could pull everything inward and make the universe collapse but, looking at it historically, it's not clear what was there in the space which would push everything outward resulting into expanding universe. Around 1920s it was not thought that space had any inherent energy which would push the matter such as galaxies apart. Yes, Einstein's space-time was dynamic which could bend, ripple, twist, etc. but it didn't have any inherent energy. By the way, if it had its own energy, it would also result into gravity. So, what was there in Einstein's equations which predicted or implied expanding universe? I think the answer lies not in the math. Also note that Big Bang theory was formulated around 1931.

Einstein was trying to come up with a cosmology model for the universe using his gravitational field equations and it required few assumptions to start with; I think the term is initial conditions. He could either have assumed that, for some unknown reason, the universe is expanding which also counteracted the attractive gravity, or the universe was static and this would require some fixed outward force to counteract the gravity. Einstein went for the static universe because this was the most prevalent view of the universe at that time though, as I've read, mathematically, not very stable. In short, it wasn't that the math itself was implying something, it was more about the assumptions used to come up with the model. Please see the excerpt below.

In the early 20th century the common worldview held that the universe is static — more or less the same throughout eternity. Einstein expressed the general opinion in 1917 after de Sitter produced equations that could describe a universe that was expanding, a universe with a beginning. Einstein wrote him that "This circumstance irritates me." In another letter, Einstein added: "To admit such possibilities seems senseless."

In his gravitational field equations, Einstein was just then providing a compact mathematical tool that could describe the general configuration of matter and space taking the universe as a whole. The peculiar curvature of space predicted in the equations was quickly endorsed in famous experiments, and by the early 1920s most leading scientists agreed that Einstein's field equations could make a foundation for cosmology. The only problem was that finding a solution to these simple equations — that is, producing a model of the universe — was a mathematical nightmare. ...

Einstein met with de Sitter in neutral Holland. Stimulating and criticizing each other, they produced two cosmological models, two different solutions to the field equations. But both models seemed to need special adjustments.

Einstein's first try at a model likewise could not contain matter and be stable. For the equations showed that if the universe was static at the outset, the gravitational attraction of the matter would make it all collapse in upon itself. That seemed ridiculous, for there was no reason to suppose that space was so unstable.

Einstein found he could stabilize his model by adding a simple constant term to the equations. If this constant was not zero, the model would not have to collapse under its own gravity. This "cosmological constant," Einstein admitted, was only "a hypothetical term." It was "not required by the theory as such nor did it seem natural from a theoretical point of view." In fact, "The term is necessary only for the purpose of making possible a quasi-static distribution of matter."

Source: https://history.aip.org/exhibits/cosmology/ideas/expanding.htm

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    $\begingroup$ Arguably the “biggest blunder” was not Einstein's but Newton's who was certain that the universe uniformly filled with matter would remain static in his (Newtonian) gravitation theory. In fact, (infinite) universe must be either expanding or contracting even in Newtonian theory. $\endgroup$ – A.V.S. Dec 24 '20 at 12:59
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    $\begingroup$ @A.V.S. : I don't think the "evolution of an infinite distribution of mass" problem is well-posed in Newtonian theory. $\endgroup$ – Jerry Schirmer Dec 26 '20 at 4:08
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    $\begingroup$ @JerrySchirmer Newton's argument was infinitary in origin: “But if the matter was evenly disposed throughout an infinite space, it could never convene into one mass, but some of it would convene into one mass, and some into another, so as to make an infinite number of great masses, scattered, at great distances, from one to another, throughout all that infinite space. And thus might the sun and fixed stars be formed…” (Newton's letter to Bentley). There is no way to “regularize” metastable finite distribution of matter without abandoning Newton's law of gravity. $\endgroup$ – A.V.S. Dec 26 '20 at 17:24
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    $\begingroup$ @JerrySchirmer: … the problem is ill-posed If you are referring to the problem that you are trying to pose, it probably is. Newton's problem with spatially infinite mass distribution, OTOH, is perfectly OK, and, like I said, Newton made an error not in posing it but in discussing its solutions, an error that is present in the above quote. $\endgroup$ – A.V.S. Dec 28 '20 at 5:16
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    $\begingroup$ @A.V.S. you have to modifiy newtonian theory somehow to deal with an infinite, potentially non-static mass distribution. The fact that you cite "geometricizing the theory" above as a potential way of showing your result shows that you acknowledge this. There are several ways of doing the modification to make the problem well-posed, and the answer you get depends on your choice. $\endgroup$ – Jerry Schirmer Dec 28 '20 at 16:34
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I'll try and briefly run through some points (without mathematical detail) to see if this clears up any of your questions

• You seem to have misunderstood the 'blunder' part: the 'blunder' wasn't removing the cosmological constant, but adding it to his equations (in an ad-hoc way, at the time) in the first place.

• Today, dark energy isn't 'different' from the cosmological constant - the CC is just a possible (and the simplest) way to describe dark energy. (It's also the one that works best, despite the surrounding theoretical issues.)

• Einstein removed the CC because it was no longer needed for a static universe (and the other associated problems regarding stability, which you quoted).

Just to be clear, neither a cosmological constant nor any type of dark energy is needed for an expanding universe, but is needed for accelerated expansion. The universe was already expanding from the big bang. A universe where the CC is zero still expands.

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    $\begingroup$ With zero cosmological constant it is still perfectly possible for the universe to expand indefinitely. In fact one of the main expected outcomes of measuring the deceleration constant was determining whether their would be a Big Crunch. $\endgroup$ – mmeent Dec 24 '20 at 12:44
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    $\begingroup$ Ah thanks for the correction, I've edited my answer. I meant that it still expands at least for some finite time in general, but what I said was definitely wrong, cheers. $\endgroup$ – Eletie Dec 24 '20 at 13:00
  • $\begingroup$ @Eletie I've accepted your answer but honestly I'd need to edit my original question and expand it. I've so many closely related questions. I'm trying to figure out how to weave all the queries into one single coherent piece. Thank you! $\endgroup$ – PG1995 Dec 25 '20 at 8:53
  • $\begingroup$ @PG1995 That's fine - it may be easier to ask followups as new, shorter questions (and you can link this question in the new one as a reference). But you're welcome! $\endgroup$ – Eletie Dec 25 '20 at 8:56
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    $\begingroup$ @PG1995 you shouldn't edit the question so substantially that it requires different answers, so what I mean is to perhaps ask that as a new question. But just a quick answer, you say it's not clear what was there in the space which would push everything outward resulting into expanding universe - there doesn't need to be anything additional in space to cause it to expand. Models of cosmology where the cosmological constant isn't there still all have an initially expanding phase. The field equations by themselves imply a dynamic, expanding universe (for some period of time). $\endgroup$ – Eletie Dec 25 '20 at 12:39

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