> Einstein originally introduced the concept in 1917 [2] to counterbalance the effects of gravity and achieve a static universe, a notion which was the accepted view at the time. Einstein abandoned the concept in 1931 after Hubble's discovery of the expanding universe.
> 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 red shift—as his "biggest blunder".
It was actually a double-blunder. Einstein missed the opportunity to predict the expanding universe (and, as a corollary, the big bang). And then, when it turned out the universe was expanding, he retracted the CC despite the fact that it actually turned out that there is a (non-zero) CC, the expanding universe notwithstanding. He got the right answer, but he abandoned it because he got it for the wrong reason.
I think you have that backwards. Physics doesn’t arise from mathematics; reality just is and the math describes it. The universe is expanding, and the cosmological constant simply describes this relationship between space and the matter inhabiting it.
Exactly right. Einstein had no idea what the physical mechanism behind the CC might be (and we still don't). It was just something he threw into the equations because he believed the universe was static, and the only way to make GR support a static universe is with a non-zero CC.
Actually, a cosmological constant is derivable from the Standard Model. But it's off by a very remarkable amount. Dark energy is the observation that that the Standard Model mispredicts the cosmological constant, so there must be something wrong with it.
> cosmological constant is derivable from the Standard Model.
Well.. not really directly "derivable."
To be more specific, the "problem" is: when using the the "Standard Model of particle physics" (which is confirmed time and again for anything we do with the particles, and which, of course, we anyway know that is still inconsistent with the General Relativity model) to calculate the "renormalized value of the zero-point vacuum energy density" as the contribution to the cosmological constant, the number is calculated that, to our present understanding of the factors involved, can't match our cosmological measurements. Note that that "renormalization" process is a method used otherwise to "extract" the finite answer from the divergent expression (i.e. one that would involve infinities). Applying such method in this derivations gets the "wrong" number.
It's much less surprising when it is stated precisely. Attempting specific derivations in which the "infinities" are "avoided" by using a specific approach which for some other cases works, we discover that in these derivations the mentioned approach "doesn't work", that is, that something is missing in an attempt to compare two theories for which we anyway know that they aren't consistent when they have to be applied together.
Luckily, these inconsistencies aren't something that prevents us to use both General Relativity and the Standard Model independently to great success. Using them together is needed only to model very extreme conditions like writing the equations for some point inside of the black hole or something like that. And that doesn't disprove black holes in any way: we measured even their collisions(!) using the predictions of the models.
> Einstein originally introduced the concept in 1917 [2] to counterbalance the effects of gravity and achieve a static universe, a notion which was the accepted view at the time. Einstein abandoned the concept in 1931 after Hubble's discovery of the expanding universe.
> 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 red shift—as his "biggest blunder".