I'm confused about the cosmological constant (CC, Λ). I assumed Einstein only included Λ to correct his General Theory of Relativity because the prevailing view at the time was that the universe was static. I thought Λ was later removed (completely) only when Hubble showed the universe was actually expanding.
WRT dark energy, some science writers put forth the claim that Einstein always had a CC from the very beginning of GR Theory, but soon changed it to reflect a static universe, then changed it again to revert to an expanding universe.
What then is the true history of the CC?
Einstein's Cosmological Constant
Einstein's Cosmological Constant
RJ Emery
I think Einstein is somewhat "worshipped" at this point, RJ. Basically, a hypothetical force introduced by Einstein into GR that had no basis in observation seems to have been realized by an observable force called dark energy.
It's neat to think that Einstein "saw it coming," but yeah, it's a sloppy match.
And since we really don't as of yet understand dark energy, I think we are jumping to conclusions...
It's neat to think that Einstein "saw it coming," but yeah, it's a sloppy match.
And since we really don't as of yet understand dark energy, I think we are jumping to conclusions...
I don't think Einstein introduced anything of the kind. I believe his equations naturally led to an expanding universe, and so he included the CC to retard that expansion, in keeping with observations and thought of the time.Orca wrote:... Basically, a hypothetical force introduced by Einstein into GR that had no basis in observation seems to have been realized by an observable force called dark energy. ...
The CC (with a different sign) has been re-introduced only because the expansion naturally predicted by GR is insufficient to match the accelerating expansion currently being observed.
However, not being an expert on GR, these aforementioned statements of mine are exactly which I seek to confirm.
RJ Emery
The nature of 'dark energy' (which is a shorthand anyway) is poorly constrained by observation, to date.
However, GR is extremely well tested, by experiments and observations, and is the core theory in modern cosmological models.
So, when a new cosmological effect is observed, conservative scientists bring out Occam's razor, and add to the highly successful model they have built the minimum of new terms.
The most general such is "w", the characteristic number of the equation of state of a perfect fluid (in GR).
Einstein's cosmological constant is w = -1.
There are other possibilities, for example quintessence.
As most cosmologists, being scientists, are keen to test these ideas, they look for ways to constrain the range of parameters such as w, by constructing quantitative hypotheses, and analysing vast amounts of data (using powerful statistical techniques). Such hypotheses also guide them in writing proposals for 'telescope time' - a proposal which can show how the telescope time will likely lead to a new (set of) constraint(s) on w (or 'dark energy') has a better chance of being approved than a 'I think it'd be cool to just look {here} for {lots of hours}' (I'm turning up the contrast, of course).
However, GR is extremely well tested, by experiments and observations, and is the core theory in modern cosmological models.
So, when a new cosmological effect is observed, conservative scientists bring out Occam's razor, and add to the highly successful model they have built the minimum of new terms.
The most general such is "w", the characteristic number of the equation of state of a perfect fluid (in GR).
Einstein's cosmological constant is w = -1.
There are other possibilities, for example quintessence.
As most cosmologists, being scientists, are keen to test these ideas, they look for ways to constrain the range of parameters such as w, by constructing quantitative hypotheses, and analysing vast amounts of data (using powerful statistical techniques). Such hypotheses also guide them in writing proposals for 'telescope time' - a proposal which can show how the telescope time will likely lead to a new (set of) constraint(s) on w (or 'dark energy') has a better chance of being approved than a 'I think it'd be cool to just look {here} for {lots of hours}' (I'm turning up the contrast, of course).
It is (represented by Λ); w is a parameter in the equation of state.RJ Emery wrote:Whoa! I thought the CC was represented by Λ. If its value is now -1 due to the accelerating universe, was it a) +1 when the universe was thought to be static and b) zero when the universe was found to be expanding?Nereid wrote:... Einstein's cosmological constant is w = -1. ...
(Perhaps I should have said "Einstein's cosmological constant is EQUIVALENT TO w = -1"?)
Did you read the wikipedia page to which I provided a link? I think that covers the relationship between Λ and w well - if you have questions after reading that, please ask away!
Yes and no. Yes, I did read it. No, I did not understand it (both the article and the equation of state).Nereid wrote:It is (represented by Λ); w is a parameter in the equation of state. ... Did you read the wikipedia page to which I provided a link?
To my knowledge, Quintessence is something originally postulated by Paul Steinhardt when he was at the Univ. of Pennsylvania (he is now at Princeton Univ.) and postulated before the accelerating expansion of the universe was discovered.
I do know that before the results of the two supernova research projects were announced, preliminary findings were circulating among astrophysicists. By way of example, some years ago I attended a lecture given by Philip Morrison of MIT, apparently knowing about these preliminary results, who said in effect Einstein's greatest blunder was in taking Λ out of GR.
I do not know what prompted Steinhardt to propose Quintessence in the first place if an accelerating expansion was not known to him or others at the time.
Perhaps both Morrison and Steinhardt were associated in some way with either Saul Perlmutter's Supernova Cosmology Project or Brian Schmidt's High Z Supernova Search Team.
Nevertheless, we are getting farther afield of my original query: Was Λ a part of GR when Einstein originally conceived of it? Was Λ included solely to make GR conform to a static universe?
It is clear that Λ is now being used to adjust GR to account for the accelerating universe, albeit Λ is now with an opposite sign.
RJ Emery
On the history, I really couldn't say.RJ Emery wrote:Yes and no. Yes, I did read it. No, I did not understand it (both the article and the equation of state).Nereid wrote:It is (represented by Λ); w is a parameter in the equation of state. ... Did you read the wikipedia page to which I provided a link?
To my knowledge, Quintessence is something originally postulated by Paul Steinhardt when he was at the Univ. of Pennsylvania (he is now at Princeton Univ.) and postulated before the accelerating expansion of the universe was discovered.
I do know that before the results of the two supernova research projects were announced, preliminary findings were circulating among astrophysicists. By way of example, some years ago I attended a lecture given by Philip Morrison of MIT, apparently knowing about these preliminary results, who said in effect Einstein's greatest blunder was in taking Λ out of GR.
I do not know what prompted Steinhardt to propose Quintessence in the first place if an accelerating expansion was not known to him or others at the time.
Perhaps both Morrison and Steinhardt were associated in some way with either Saul Perlmutter's Supernova Cosmology Project or Brian Schmidt's High Z Supernova Search Team.
Nevertheless, we are getting farther afield of my original query: Was Λ a part of GR when Einstein originally conceived of it? Was Λ included solely to make GR conform to a static universe?
It is clear that Λ is now being used to adjust GR to account for the accelerating universe, albeit Λ is now with an opposite sign.
On the use of w, and its role in being the 'lightning rod' for testing ideas on 'dark energy': AFAIK, that's the simplest way to do the tests - crunching the observational data will give you an estimate of w, plus error bars ... and w is 'theory blind', in the sense that it's just a parameter in an equation (specific theories will have specific values of w; the cosmological constant gives w = -1, for example, and quintessence a value other than -1).