Talk:Cosmological constant

Old comment
I think what the author meant is that is unclear that current observations are due to a cosmological constant, or a cosmological "variable", i.e, not a constant term, is that so?

What are the units of &Lambda;?
Basic SI unit analysis does not support s2 as valid units for this equation.

The SI units are as follows:

G = m3 kg-1 s-2

$$\rho_{vac}$$ = N m m-3

c2 = m2 s-2

When this is all cancelled out you get m-2 AH 21:27 28th August 2006 (GMT)

The article first says sec2 and then later J4. AxelBoldt

The units are sec-2. The article is correct now (I realize that the above question was asked a long time ago). Merenta 16:44, 16 Nov 2004 (UTC)

Actually the original units are m-2.

Originally Λ, that was equal 4πGρ/c2, where ρ was density of space in [kg/m3], was the curvature of space of stationary universe, or Λ=1/R2, where R was so called "Einstein's radius of the universe" (in [m] and that's why Λ was in [m-2]). However, since the nature of Λ is still a subject of debate, the units are irrelevant and everybody is free to express Λ in units supplied by his/her pet theory. People who don't believe Einstein's theory of gravitation even interpret it as "repulsive gravitational force" (and then they probably express it in [kgm/s2]). This interpretation is not possible in Einstein's gravitation since there are no gravitational forces acting at distance (repulsive or otherwise) and the gravitation is just an expression of geometry of spacetime. But if one likes ρ to be density of energy rather than density of mass then of course the units are s-2. Of course it requires dividing Λ by c2 and the rest of Einstein's equations is nicely recovered. Jim 20:41, 24 Nov 2004 (UTC)

Safe enough, of course, since relativists typically set c=1 and don't bother distinguishing between metres and seconds any more!

Pushing around factors of the speed of light and Planck's constant the most popular units for the cosmological constant seem to be Planck units, GeV4 and g/cm3. --Joke137 01:20, 5 Feb 2005 (UTC)


 * okay so i might be wrong since i normally work in natural units until it comes time for data analysis, but shouldnt it be c^2 instead of c^4. Now i know it says energy density, but in my workive only seen it written in cgs units of g/cm^3; regardless of its radiation or matter or whatever(shouldnt matter).  So even though we are talking about energy density its usually "spelled out" in these units.  However i can see if you state the density to the equivalent of eV/m^3 you would need c^4.  its just odd since i never see it written like that but maybe im in a weird nitch of cosmology research ?? its not important since c is just a factor but i thought i might point it out --Blckavnger 23:06, 27 November 2006 (UTC)

If it is being called an energy density then it must have c^4.


 * Sounds good to me ... its not important since its not engineering or something like that. Just like mass of electrons is always reported in terms of MeV even though its mass.  It just looked wrong at first glance since ive never seen it to the 4th power in any paper or textbook ive used; of course ive just might have forgotten with all papers ive stumbled through in the past.


 * the fact that people still seem to want to change the power of c means we need to clarify the units. just cuz we are saying energy density versus mass density doesnt mean much, especially to people who work with relativity. (you could argue mass is more fundamental since its scalar where as energy is component of momentum 4 vector).  whether it be to the 4th or 2nd doesnt really matter, in terms of the physics.  we just need to be clear so we avoid back-and-forth edits.--Blckavnger 16:47, 6 December 2006 (UTC)


 * looks better but still a little confusing becuase the subscript should still be the same since its the density of the vaccuum, what changes is the units ... i just see a possiblity for confusion, id change it but im still a newbie to wiki. —The preceding unsigned comment was added by Blckavnger (talk • contribs) 17:04, 7 December 2006 (UTC).


 * I took care of it. — DAGwyn 23:37, 8 December 2006 (UTC)

I think the explanation about `for historical reasons' as stated in the opening paragraphs is unclear. Is the factor $$8\pi$$ for historical reasons, or is the dropping of the G and c terms for historial reasons? If the former it seems that the word 'density' is being redefined: rather than meaning per unit volume (the ordinary meaning, where your unit of volume is length unit$$^3$$) to meaning perhaps per $$1/(8\pi)$$ of whatever you unit of volume is. Very confusing to me to have a length unit $$L$$ and not have the volume unit equal to $$L^3$$, so perhaps I have misunderstood. Note I am just asking for a clearer staement in the article of what is going on? Do you have to say `can be though of as the energy density ...'? What is wrong with `is proportional to the energy density ...' E4mmacro 22:49, 4 April 2007 (UTC)


 * I appreciate your comments and largely agree with the gist of them. A problem we have with this article is that it is hard to arrive at a consensus; the current state reflects the best balance we have come up with so far.  Note that there are other Wikipedia articles that touch on the same subject, so when I added the formula recently I tried to maintain consistency with them.  The original cosmological constant was introduced by Einstein just as the equation shows, except he lumped together the factors of the tensor T into just "κ".  The 8π, G, c stuff comes from working out the Schwarzschild solution and identifying its asymptotic form with the Newtonian formula for a gravitational point source, with no special units assumed.  (Actually when I worked it out decades ago I got 4π instead of 8π; either I made a mistake or all those guys repeating the formula are promulgating somebody else's mistake.)  Many workers these days simplify things by adopting more convenient units where c=1 and/or G=1.  The 8π remains as essentially a geometric factor, tied to a "historical" convention only in that the "more convenient" units could have assimilated the 8π also, but didn't.
 * As to "thought of as", I believe it is important to express the situation that way. The notion that Λ is the vacuum density arises as follows:  (1) start with Einstein's equation with cosmological term, which at this point is connected with space-time structure, not with matter; (2) convert to equation for "empty space" by setting T=0; (3) move the cosmological term to the right-hand side; (4) interpret the result as conventional general relativity without a cosmological term, but with what started out as that term now interpreted as the T tensor.  I.e., the vacuum density interpretation is logically distinct from the original intent of the cosmological constant.  There are related issues when the constant arises in other contexts, such as Schrödinger's formulation of unified field theory.  Therefore, saying that the constant is the vacuum density would be to enforce only one particular interpretation.  "Can be thought of as" is not only correct, it also hints that there are other ways of thinking about it (which is also correct).
 * If you think you can improve the exposition without breaking anything (including consensus), feel free to do so. If you want to suggest changes here instead, they will probably be seen by the people who most care about the content of the article and thus eventually lead to article edits. — DAGwyn 22:34, 5 April 2007 (UTC)

Thanks for that. I wonder if the word "essentially" is necessary? "essentially the energy density"? E4mmacro 06:42, 6 April 2007 (UTC)


 * Good point. I made changes based on the foregoing; it seems to read better now. See what you think. — DAGwyn 19:02, 6 April 2007 (UTC)

Reinstating c?
The previous changes look good to me, DAGwyn. I am trying to understand this better and I notice that on the Friedmann equation page there is an equation with c and G in it, (the first Friedmann equation, written in what they call Hubble constant form). This equation which appears to me to be missing a factor of $$ c^2$$. The LHS is $$\dot{a}^2/a^2$$ which has dimensions of $$T^{-2}$$ (unless everything is non-dimensional). This has to match the dimensions of $$G\rho$$ on the RHS. It seems to me it should be $$G\rho/c^2$$ which has the required dimensions $$T^{-2}$$. I am not a big fan of units which make $$c=1$$ in this context; it seems very difficult for a beginner (someone reading wikipedia trying to learn) and has confused me somewhat, for example. If one is going to write non-dimensional terms, which is fine, I think there needs to be a clear statement about it; i.e. a = r/r0 where r is a distance and r0 is a reference length; v = u/c where u is a speed and so on. It could be just as easy to re-insert all the symbols for c, and anything elsewhere `missing', becasue of non-dimensionalization? Maybe someone can look at it? Thanks. E4mmacro 04:37, 7 April 2007 (UTC) By the way. I realise that ever since Poincare 1905, reinstaing c into relativity equations could be said to be a retrograd step. My point is that the typical wiki reader of this article dosen't need the extra apparent complication. E4mmacro 21:34, 7 April 2007 (UTC)
 * I see that if $$\rho$$ is mass-density (not energy density as I originally thought and as it is on the cosmological constant page), $$G\rho$$ has units of $$T^{-2}$$ as requried. E4mmacro 22:05, 9 April 2007 (UTC)
 * There is a discussion of that above ("What are the units of Λ?"). Units are problematic when various differently defined quantities are being related to each other.  I excised the statement of units from the article, which seems just fine without it. —  DAGwyn 19:14, 10 April 2007 (UTC)

I have just clarified (in the article) the connection with energy density and pressure. I also added an early note giving an upper limit for the value of the constant (using km-2 units, which are appropriate at that stage) based on a reference that provides a comprehensive survey and statistical analysis. — DAGwyn 01:41, 14 April 2007 (UTC)

This commant fits maybe in here: I think it is a good idea to insert c and (especially) G. This sentence should be modified: "The cosmological constant has the same effect as an intrinsic energy density of the vacuum, ρvac (and an associated pressure). In this context it is commonly moved onto the right-hand side of the equation, and defined with a proportionality factor of 8: Λ = 8ρvac, where unit conventions of general relativity are used (otherwise factors of G and c would also appear" as G and c are already mentioned in the equation above. I tried to edit it and it was reverted. -- 129.240.190.125 (talk) 16:44, 27 April 2013 (UTC)
 * The edit summary of the revert is worth reading: I'm not against introducing c and G, but then the rest of the sentence should be kept consistent with that. That is, we shouldn't explain why we omit something we don't actually omit. Btw: why did you re-introduce only G, but not c? &mdash;&thinsp; H HHIPPO  20:23, 27 April 2013 (UTC)

Inaccuracy in article?

 * Because the cosmological constant has negative pressure, according to general relativity a positive cosmological constant--which means empty space has positive energy--causes the expansion (or contraction) of empty space to accelerate.

(Emphasis mine.) I don't know enough about the topic to remove the bolded part, nor can I find good enough material online (grumble). But from my understanding, isn't a positive CC expansion and a negative CC contraction? -- Wisq 16:57, 2005 Feb 23 (UTC)


 * It's alright, but perhaps not totally transparent:
 * positive cosmologicla constant <=> positive energy <=> negative pressure
 * Pjacobi 01:00, 2005 Feb 24 (UTC)


 * Okay, but my question is, could a positive cosmological constant equal contraction? It seemed to me that positive constant = negative vacuum (expansion), while negative constant = positive vacuum (contraction)... if so, then saying "positive constant means expansion (or contraction)" would be inaccurate. -- Wisq 03:32, 2005 Feb 24 (UTC)


 * postive constant gives an extra negative pressure term, but if the normal and dark matter outweight that term, the universe would still collapse (it would never reach the regime of exponential expansion, characteristci for positive c.c. (this is thought to be ruled out by current observations)
 * Pjacobi 10:01, 2005 Feb 24 (UTC)


 * I think I put that in. It is both inaccurate and confusing. A universe with a c.c. can either be expanding or contracting (although it won't switch from one to the other). Both the expansion and contraction are exponential, but it doesn't really make sense to say that the contraction is "accelerating." --Joke137 16:20, 24 Feb 2005 (UTC)


 * What you are saying applies to universe without any matter. A matter with a positive cosmological constant small compared to the matter content, can expand and than contract. --Pjacobi 19:03, 2005 Feb 24 (UTC)


 * No, because the matter will red-shift away and the c.c. will eventually dominate. That is what is happening in our own universe. --Joke137 19:22, 24 Feb 2005 (UTC)


 * Just add enought matter, eventuell the solution will show recollapse before the c.c. has a chance to dominate, see for some calculations. Of course, as said above, this setting is pretty musch ruled out for our universe. --Pjacobi 20:02, 2005 Feb 24 (UTC)


 * Oh, if you allow curvature I agree. I was assuming $$\Omega_k=0$$ --Joke137 20:35, 24 Feb 2005 (UTC)


 * I too am puzzled by this. We are told that a positive cosmological constant <=> positive energy <=> negative pressure and that this drives the expansion of our universe. But in the section on negative pressure (in the Pressure article) all the other examples of negative pressure are a kind of suction, causing things to pull inwards - a shrinking force. Yet here we are being asked to believe that negative pressure is driving an expansion. How can this apparent gross contradiction be resolved? &mdash; Cheers, Steelpillow (Talk) 09:27, 16 September 2016 (UTC)


 * This is a good question. The negative pressure does not result in any suction in the sense you are talking about, because it is equal everywhere, so there is no pressure differential. It is the "gravity caused by" the energy that accelerates expansion.


 * But what does that mean exactly? I don't really know either. But one way of describing de Sitter space, which is an empty universe which a positive cosmological constant, is as an inside-out black hole. Mathematically, the static co-ordinates of de Sitter space and the static co-ordinates of a non-rotating black hole are very similar. They have spherical event horizons, but for a black hole we are on the outside of the sphere, for de Sitter space we are on the inside. The "event horizon" of the universe is called the cosmological horizon. --174.116.141.16 (talk) 04:50, 22 September 2016 (UTC)
 * I use "suction" loosely in the same way that "pressure" is used loosely and the same semantics apply. Intuitively, positive internal pressure makes things expand and negative internal pressure (suction) makes things contract. Intuitively, if you want to make a universe expand you would pump it up with positive pressure. Here we are being presented with negative pressure as an intuitive analogy for the cosmological constant yet it is behaving counter-intuitively. What use is an analogy like that? How can we get past its self-contradiction to something meaningful? What would make a de Sitter space intrinsically expand itself - grow its internal distances - rather than by throwing objects into its event horizon? &mdash; Cheers, Steelpillow (Talk) 09:06, 22 September 2016 (UTC)


 * "positive internal prsesure makes things expand and negative internal pressure makes things contract". Right, internal. What about external? You could say: "positive external pressure makes thing contract and negative external pressure makes things expand". Right?


 * "Here we are being presented with negative pressure as an intuitive analogy" Valid complaint. I mean, I suppose you could say that we are being "sucked out" of the cosmological horizon instead of "sucked in" to a black hole event horizon, but I'm not sure that's at all helpful.


 * Analogy aside, there literally is a negative pressure. It does not actually cause things to expand or contract in and of itself, because it is equal everywhere, internally and externally. What happens is that, according to general relativity, it is not just mass that causes gravity, but also momentum and pressure.


 * There are some technical details on the page, but also a template that we asks we "make it understandable to non-experts, without removing the technical details. The talk page may contain suggestions." okay, here are some suggestions :-)


 * The cosmological constant can be thought of as "dark energy that has the exact same density, everywhere, always" and we may want to reshuffle between the two articles a bit. (I did a very little bit of this already.)


 * General relativity predicts momentum and pressure cause gravity, but for ordinary matter, it's not noticeable. For example, the Earth's rotation was predicted to cause a slight frame dragging effect. This effect is now measurable with current technology, just barely. It is tiny compared to the Earth's ordinary gravitational attraction. But it is there, and it contradicts Newton's theory of gravity, according to which a) rotation should not produce gravity, and b) there should be no such thing as "sideways gravity".


 * For extraordinary objects, this would be noticeable. A rapidly spinning black hole is predicted to have a much different gravitational field than a stationary black hole of equal mass. It not only pulls you inward, but also very strongly drags you sideways along with its rotation, even at a distance.


 * Now dark energy is also very far from ordinary matter. The gravitational effect of its pressure is the source of the expansion we are talking about. Maybe it is better to just think of it as a weird effect of relativity, like frame dragging, and not in terms of sucking and blowing analogies.


 * Dark energy is energy, and energy is mass, and this mass does have an ordinary gravitational attraction. Just that the extraordinary gravitational field from pressure is three times stronger. But it is not just in the opposite direction to ordinary gravity: if you had a mixture of exactly one part dark energy to two parts ordinary matter, the attractive and repulsive parts would cancel, but there would still be a gravitational effect. It would be neither attractive, nor repulsive, nor even "sideways", but purely "warping".


 * History: that exactly balanced mixture was Einstein's original model for the cosmological constant, which results in a curved, finite, static universe. This model is wrong and was abandoned for various reasons covered.


 * --174.116.141.16 (talk) 08:48, 23 September 2016 (UTC)
 * Thank you. I think that relativity's prediction that pressure and momentum also create gravity needs bringing forward. But it is still not obvious how gravity might change the size of the universe, as opposed to making energetic stuff attract and repeal other stuff inside a constant-volume universe. There is nominally no "outside" to "suck". I suppose it's the scale equivalent of the rotational difference between a Newtonian orbit and frame-dragging? &mdash; Cheers, Steelpillow (Talk) 12:12, 23 September 2016 (UTC)


 * "Scale equivalent of frame-dragging"... it'd be nice to have a standard example that is to pressure what frame-dragging is to rotation. I'm afraid the standard example is the cosmological constant itself. So that's useless here :-)


 * It's worth mentioning that the change-the-size-of-the-universe business happens without a CC. It is true that the CC does accelerate it. The expansion of the universe article explains some. The de Sitter universe article does mention there's a way of taking co-ordinates in de Sitter space that makes it static, so "repel other stuff in a constant-volume universe" isn't really wrong in the de Sitter universe. You can't take static co-ordinates in our universe, but the point is, that's not exactly the fault of the CC. Sadly it looks like the two articles I linked need some help too. --174.116.141.16 (talk) 00:20, 4 October 2016 (UTC)

Fine-tuning
I find it dishonest to speak about fine-tuning without qualifying the statements, but I don't know how to add this properly. I am watching "What we still don't know" documentary right now and they go out of their way to express how unlikely coincidence would that be to have the cosmological constant fine-tuned to 10^120th. But what we must note is that our understanding of this area of physics is still not final. It's not like we are already sure about the way expansion works. Even more important is that there may be no fine-tuning involved at all - we are just looking at the problem in the wrong way.

For example, I can claim that there is a remarkable finetuning of a certain variable for each couple - if that variable wasn't correctly set to 1 part in 10 million, there would be no conception or the mother would die. What that variable is? It's the number of dead sperms. If the difference between that number and the number of total produced sperms is more than, say, 10, the mother would explode, as its womb tries to produce 10 babies. :) If the difference is 0, no child will be born.

That BS, because the limiting factor to the number of babies conceived is the number of ova ready to be fertilized, not the number of sperms. In fact there are millions of live sperms in each ejaculation, but since only one sperm can fertilize each ovum, and usually only one (rarely two, and more than that usually only due to hormonal treatment) ova are available in each period, only one (rarely two or more) sperm succeeds. No danger of explosions here at all! 142.3.164.195 23:12, 6 March 2006 (UTC)

This is essentially the same as claiming that one term of the cosmological constant should be fine-tuned to differ from another term by a particular small amount. This is a wrong way of looking at the picture. For example, the number of people who are not Queen of the United Kingdom needs to be fine-tuned to the precision of 1 part in 6.4 billion. If that number was smaller than needed, there would be several Queens of the UK, which would lead to a significan confusion. If that number was bigger than needed, there would either be no Queen, which would cause chaos (at least in the British yellow press) or a negative number of them, which would be a huge violation of decorum and a scandal (which might cause chaos too, because of the coverage in the yellow press). Just like with the cosmological constant, I can say that a huge "Queen constant" is predicted by the world demographics and it needs to "be cancelled almost, but not exactly, by an equally large term of the opposite sign". Paranoid 8 July 2005 22:38 (UTC)

The whole usage of the word fine-tuning is biased here. Firstly, as there is no (consistent) quantum theory agreeing with a cosmological constant, the question of it being even a parameter is open. It could just be an experimental value in a certain limit of a complete theory. The second reason is explained in the arcticle to fine-tuning itself: The credibility of a model that needs fine-tuned parameters is by default not too high, as it lacks the explanation for why the value happens to have exactly the needed value. 109.208.177.253 (talk) 12:33, 14 August 2013 (UTC)

Decreasing for a trillion years?
There's some interesting news out today that Paul Steinhardt at Princeton University, and Neil Turok at Cambridge University are hypothesizing the age of the universe to be about a trillion years (after it's been through a series of big bangs and crunches), allowing for the cosmological constant to decrease over time. Of course, I'm not sure how to work the theory into the article ;-) -- ke4roh 20:40, 5 May 2006 (UTC)

Whither the vacuum energy ?
When people talk about the vacuum energy (aka the Zero Point energy) they're referring to an effect and the formulae that come from understanding it. Or, rather, figuring out that it exists at all. I wonder if anyone has considered and discussed a few facts relevent to the topic ?

All "particles" have an associated field. These fields extend to the edges of the universe. All sorts of energy go into this field (a. Space is large. b. space is really large. c. all "fields" does not mean some "fields"). Interactions of "particles" that produce new "particles" do not create new fields, simply rearrange existing fields (else why would all "particles" decay into other "particles"?). Note: Part of this problem is people are still thinking about "particles", which don't really exist. Replace "particle" with "probability locus" and you're closer.

This makes up the energy of the "Virtual Field" Prof. Hawking mentions as where particles near black holes are produced as well as the source of what we perceive as gravity and inertia.

The "energy" we see in this field can't be drawn upon without some localized energy input (like a black hole in the process of swallowing matter, say) and then only what the gradient allows.

It seems to me that if energy can't be drawn from the field because it has no pressure behind it (think of this energy like a really large room with a few weak fountains of water in it and a floor covered with a shallow layer of water - this shallow layer of water is the energy referred to here), then there is nothing left over to power a bigger CC. It could explain the perception of so called "dark matter" and be responsible for the apparent "accelleration" of spatial expansion.

Static universe solution
The "General relativity" section of the article states:

"Also, a static-universe solution to the original field equations was discovered, so it was not necessary after all to add the extra term in order to achieve such a solution."

Is this correct? What is the name of the solution, as I haven't heard it referred to elsewhere? --Christopher Thomas 23:06, 28 August 2006 (UTC)


 * Neither have I. In fact, I am sure no such thing exists, so I removed the sentence. I think I have run into this particular misconception before on Wikipedia, but I can't remember where... –Joke 03:07, 29 August 2006 (UTC)


 * It's not a misconception, but what Einstein himself stated. I restored the reference in a different way that ties in better to the rest of the text, along with the links to relevant existing articles. Don't be misled by the occasional modern formulation of the solution showing a cosmological constant, as the constant can be exactly zero and you still get an exact static solution (also expanding or contracting, depending on another parameter).DAGwyn 20:39, 29 August 2006 (UTC)


 * Hm, perhaps you mean a static universe with positive spatial curvature (which is also unstable)? Otherwise, there would either have to be matter with negative energy, or the universe would have to be empty. –Joke 20:45, 29 August 2006 (UTC)


 * Perhaps DAGwyn refers to Einstein's misconception that a static solution existed, but was later shown to be in error (i.e. it was shown to be unstable (by Friedman?)). --Michael C. Price talk 21:14, 29 August 2006 (UTC)

The text attributing Einstein's "biggest blunder" comment to Friedman's contribution is in error. The comment was in response to Hubble's observations of the cosmic expansion:
 * "When Albert Einstein applied his theory of general relativity to the universe the paradigm was that the universe was static. Since matter and energy gravitate, they drive the universe to collapse on itself. This was physically unacceptable, so Einstein introduced a cosmological constant term in his equations to balance the attractive force of gravity. It was latter discovered by Edwin Hubble that other galaxies appear to be moving away from us, that the universe was actually expanding. It was these observations that caused Einstein to claim that the inclusion of the cosmological constant was his biggest blunder, and was subsequently dropped from cosmological theories."

--Michael C. Price talk 21:24, 29 August 2006 (UTC)


 * I don't know why you prefer guesswork from a secondary source over Einstein's own account. Anyway, there is a serious misconception in the article in general, whether or not it reflects consensus among current workers in this field, in confusing instability of the space-time cosmological model with an assumed inability of the model to describe a stationary state.  The model embeds the time dimension and is perforce not able to change, so the instability doesn't cause the cosmology to do anything.  If a solution exists, then it is what it is and describes what it describes.  The changes I made were both historically and technically correct and should be restored since they actually explain something relevant, but if you prefer to spread misconceptions, have it your way.  DAGwyn 20:48, 30 August 2006 (UTC)


 * To say GR is static because it embeds time as a dimension is a serious misuse of language and will mislead virtually all readers. I'd be interested to see a direct quote by Einstein where he clearly attributes his "biggest blunder" confession Friedman's input.  --Michael C. Price talk 21:03, 30 August 2006 (UTC)


 * That's not at all what I said! I said that the particular cosmological model (be it Friedman's, deSitter's, or whatever) describes the whole time-evolution of the (model) universe in itself, and whether or not there are other "nearby" solutions to the field equations has no bearing on whether the particular "unstable" (more accurately, critical) solution is a possible universe.  The statement often seen (also here and in Bernstein's biography of Einstein) that the least little disturbance would cause the universe to move away from the static solution is literally nonsensical, since that whole way of talking presumes yet another time axis unrelated to the one in the model universe.
 * As to the blunder/Friedman relationship, probably the most accessible source is the Appendix for the Second Edition of "The Meaning of Relativity", which was reproduced in all subsequent editions. In that particular exposition Einstein emphasizes the connection with nonzero average density of matter rather than with a static universe, because by then the Hubble effect had been discovered.  (Much more could be said about that Appendix, but the point is that it definitely ties the removal of the cosmological term to Friedman's model.) — DAGwyn 04:43, 31 August 2006 (UTC)


 * This is nonsense. You say I have misrepresented your views on "static time" and then you go an repeat exactly what I complained about!  Any serious cosmologist can simultaneously grasp the concept of time as a dimension AKA "static" time and talk of unstable cosmological models.  --Michael C. Price talk 06:39, 31 August 2006 (UTC)


 * Excuse me, but I was working in this field since the 1960s, and did my graduate work on it. After I got my degrees, I left Physics for another profession largely because I saw that otherwise I would be continually battling this kind of lack of understanding.  If you would make the effort to understand what I did say (with careful choice of words), rather than filtering it through a contrary preconception, then perhaps we could have an intelligent discussion of the matter. — DAGwyn 05:10, 1 September 2006 (UTC)


 * I note that whilst I am accused of not understanding your point you make no further effort to explain how I have misrepresented you. --Michael C. Price talk 05:40, 1 September 2006 (UTC)


 * Since I already stated it twice in different ways, a third time doesn't seem likely to help. The fellow in the office next to mine, who isn't a physicist, understood immediately what I was saying, so I don't think the problem lies in my explanation.  Anyway, one more try using a simple-minded analogy: Suppress a spatial dimension or two and construct the model universe described by some solution of the GR field equations, and set in on the desk before you.  Now try to apply the claim "given a slight perturbation, the universe would expand/contract/oscillate/whatever": what does that mean?  All those verbs pertain to the time axis in the room containing the desk, not to the time axis marked on the model universe.  Yet they are taken as if they did apply to the universe itself.  That's just wrong!  If the model sitting on the desk was properly constructed then it does represent a "possible" universe, whether or not other models could be constructed.  Note that, being a universe, it already contains all phenomena that exist; there can be no external forces such as some total-energy minimization principle "acting on" the universe to "change" it.
 * There is a lot of really sloppy description and analysis going on in theoretical physics these days; I had to stop reading Phys Rev D because it was raising my blood pressure. — DAGwyn 07:40, 2 September 2006 (UTC)
 * Yeah, right. Following this logic we shouldn't say the universe is expanding, or indeed that anything happens at all.  --Michael C. Price talk 09:44, 2 September 2006 (UTC)
 * I see you actually haven't followed the logic. There can be expanding/contracting/oscillating/static models for the (entire) evolution of a universe, and some of them are compatible with the GR field equations, indeed some even with the source-free equations.  There are also some interesting non-GR based models, such as E. A. Milne's "kinematic relativity", which supports a static universe with a Hubble-like red shift (not due to expansion!).  But correct analysis of such models requires considerably more care than many are willing to invest. — DAGwyn 05:42, 4 September 2006 (UTC)


 * I see once again you claim I'm wrong without actually addressing the issues raised. No matter, your views are original research by your own admission.  That's all we really need to know to exclude them from Wikepedia.  --Michael C. Price talk 09:14, 4 September 2006 (UTC)


 * Far from it; the cited work by Einstein himself completely supports the mention of Friedman that is currently in the article. (The comment by Pervect below supports that.)  And I did address the stability issue, but you haven't bothered to understand the argument.  Note anyway that that is an educational matter and this isn't the proper forum for it.  Maybe you could cut and paste the whole discussion to an appropriate newsgroup and get somebody else to explain it to you. (Don't try to merely paraphrase it, since you can't do that properly when you don't understand it.) — DAGwyn 01:34, 5 September 2006 (UTC)
 * Also note the original statement to which I originally objected (I think this may have gotten lost in the argument):
 * "It is now thought that adding the cosmological constant to Einstein's equations does not lead to a 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 which contracts slightly will continue contracting. These sorts of small contractions are inevitable, due to the uneven distribution of matter throughout the universe."


 * Einstein mentions both Friedmann and Hubble in that appendix, which is available online. I would suggest mentioning them both.  While I suspect that Hubble was very much more influential than Friedmann,  your source possibly justifies including Friedmann's name as well as Hubble's.  I do not believe that your reference can be interpreted in such a manner as to leave Hubble out entirely, which seems to be your (DAGwyn)'s current position. Pervect 05:28, 31 August 2006 (UTC)


 * No, I never implied that Hubble was irrelevant, just that that wasn't the only reason why Einstein was happy to drop the cosmological constant. — DAGwyn 05:10, 1 September 2006 (UTC)


 * Do you have the online link to hand? --Michael C. Price talk 06:45, 31 August 2006 (UTC)


 * http://www.gutenberg.org/etext/5001. Bartleby.com also has a version, but it's missing the necessary appendix where this is discussed (appendix iv). Pervect 08:04, 31 August 2006 (UTC)

Thanks for the Gutenberg link. I believe the text justifies the sole inclusion of Hubble for the removal of the cosmological constant, since Einstein states he was originally strongly motivated to find a static solution with positive average density, which required the cosmological constant. Friedman, according to Einstein, demonstrated the existence of a non-static solution with positive average density, but which didn't require a cosmological constant -- but Einstein gives no indication that he accepted this as a model of the actual universe (which Einstein, along with consensus at the time, still believed to be static) until Hubble's data emerged. So it was Hubble who caused Einstein to reject the cosmological comstant, not Friedman. --Michael C. Price talk 09:29, 31 August 2006 (UTC)


 * Einstein's own presentation in the Appendix for the Second Edition heavily emphasizes Friedman's contribution. Certainly, the shift to an apparently expanding universe was instrumental in Einstein's change of mind about the need for a static universe, but if you at all understand his presentation you will see that it was the existence of a model (Friedman's), based on the original field equations, that supported a nonzero average mass density that was instrumental in convincing him that there was no need for the cosmological constant.
 * Having reviewed the source material, I'm prepared to grant that although Friedman's model does in fact have a flat (static) solution, as well as solutions for positive and negative curvature, it may not have been the static solution that Einstein really cared about by that time. I'll make another attempt at editing the article, that I hope you will be able to tolerate.  As a general principle, additional relevant information should always be welcome. — DAGwyn 05:10, 1 September 2006 (UTC)


 * Another, far more plausible, interpretation of Einstein's comments is that it was Hubble's data that persuaded Einstein to drop the cosmological constant, after which Einstein was more inclined to look sympathetically upon Friedman's work, which he had previously regarded as an non-physical mathematical solution to the field equations. --Michael C. Price talk 05:55, 1 September 2006 (UTC)


 * That may be, although there is no way to know for sure at this point. Anyway, it is consistent with my most recent edit to the article. — DAGwyn 07:40, 2 September 2006 (UTC)

Steinhardt
Is Steinhardt's idea notable enough to be included here? With some effort, it should be possible find any number of ideas why the CC is that small, but none of them gathered a sizable followship so far. --Pjacobi 14:16, 24 November 2006 (UTC)


 * In "cosmological units" the constant is 1, which puts a different slant on the question. Eddington thought that it related the (inverse of the) radius of the universe to our laboratory units of length. — DAGwyn 23:41, 26 November 2006 (UTC)

What is it?
I am not an astrophysicist or cosmologist. A point that the article, in my opinion does not clarify is, what is the cosmological constant? What does it measure? Why is it constant?


 * It's a constant of integration in the solution to the metric in general relativity. So if GR is exactly right (which it isn't) then the Cosmological constant is physically constant.  What it is physically?  Nobody knows (although there are lots of ideas...) WilyD 22:40, 21 December 2006 (UTC)

In regard to the “fine tuning problem”, why is it so unlikely that this “cosmological constant” is not casual?

Regards.


 * re "what is it?", there is now an early link to the Einstein field equations where the cosmological can be viewed in context. --Michael C. Price talk 23:19, 21 December 2006 (UTC)
 * I think what the original editor was getting at, is that the lead section fails to answer the question. It needs to be rewritten. &mdash;Viriditas | Talk 05:31, 24 February 2007 (UTC)


 * Note that this was done recently. — DAGwyn 22:40, 5 April 2007 (UTC)

Inverse Gamblers Fallacy
First, im I'm fairly inexperienced when it comes to wikipedia modifactions. Last time i deleted an innaccuracy i was told it should be reported why first. Everyone can click on the "inverse gamblers fallacy" link and see that anthropic explanations do not commit it (which some user added in to the original statement which notes that a multiverse in response to fine-tuning does commit the fallacy. So im going to fix it back to how it was before. —The preceding unsigned comment was added by Gnarlyocelot (talk • contribs) 19:03, 6 April 2007 (UTC).

Empirical evidence
This article should explain empirical evidence for or against this hypothesis, or clearly point to other article(s) that do. -- Beland (talk) 15:51, 26 February 2008 (UTC)
 * Err, a Cosmological Constant is just a term in Einstein's Equation - that the universe has a cosmological constant (or Dark Energy) is discussed at Cosmic_acceleration which is linked in the opening. Wily D 15:58, 26 February 2008 (UTC)

This article sucks. I read the entire thing and no where does it explain what the Cosmological constant actually is. No wonder it's a B class. —Preceding unsigned comment added by 24.225.59.43 (talk) 05:24, 3 March 2008 (UTC)

Unappreciative though the preceding comment is, I have to agree. How do R, g & T pertain to what they pertain to - pertaining is totally non-specific as a description of a relationship. What are the mu/nu subscripts doing, and what is being expressed by the equation - what is the term on the right, what is the term on the left, and is it somehow important or illuminating that they are equal ? —Preceding unsigned comment added by 81.2.101.220 (talk) 21:46, 23 March 2008 (UTC)

Changed section headings, created new section, expanded description of cc problem
I just came across this article. I split the section titled `general relativity' into two sections; one which seems to be logically the history of the cosmological constant and the other which deals with the measured positive cosmological constant.

I felt that the second issue -- that of a measured positive cc (according to the most popular cosmological models at least) -- definitely deserved a separate section. Moreover, `general relativity' was not very descriptive.

I also elaborated the explanation of the cc problem, explaining that we expect to get a cc of the order of M_{\rm pl}^4 and get one that is 10^{-120} orders smaller.

btw I think the numbers on this page should be checked. For example, the value of the cc is given in different units and while everything is consistent to a couple of magnitude, its not quite right. For example, 10^{-47} Gev^4 ~ 10^{-123} M_{pl}^2. This can be a source of some confusion. I didnt want to change this without checking through all the units, but if someone else has this on the tips of their fingers they should do this. cheers, Perusnarpk (talk) 20:04, 30 July 2008 (UTC)

Bad lede
Could I just take a second here to point out that the first sentence of the lede in this article does not actually say what the cosmological constant is?

It would be sort of nice if we could kinda shoehorn that in somewhere... (I see a bit on the talk page, above, suggesting that this was once corrected; it appears broken again. --Baylink (talk) 18:47, 10 September 2008 (UTC)

Corrected Missing Sign, Incorrectly Definitive Statement
Corrected missing negative sign in second sentence of second paragraph of "Cosmological constant problem" (10^-120 was incorrectly written 10^120).

Also changed: Critics note that these theories, when used as an explanation for fine-tuning, commit the inverse gambler's fallacy. To: Critics claim that these theories, when used as an explanation for fine-tuning, commit the inverse gambler's fallacy.

As whether the fallacy is committed is a matter of debate (and, for the most part, has been refuted). Does this line even need to be included? I have not heard any application of the "inverse gambler's fallacy" not addressed by the Leslie rebuttal. I.e. it is only possible to observe a fine tuned universe. Given that you know you cannot observe non-tuned systems, it is reasonable to assume that likely variations exist unobserved. Hacking's math is sound given his assumptions, but his application is flawed, even at a glance. The "inverse gambler's fallacy" is only committed if one tries to use the "fine-tuned" universe as evidence for multiple universes, not vice versa. —Preceding unsigned comment added by 24.233.77.207 (talk) 15:04, 30 October 2009 (UTC)

Multiverses
1.	What is the actual figure of the Cosmological constant?

2.	Do we have tangible evidences of existence of other universe / multiverses?

Cheers

89.211.115.190 (talk) 13:42, 10 November 2009 (UTC)

The problem of cosmological constant has been completely solved
Mechanism-Revealed Physics (36/40)

Solving the problem of cosmological constant by proving that the concept of cosmological constant in itself turns out to be mechanistically thus essentially wrong. The problem of cosmological constant has been widely recognized as one of the most fundamentally important unsolved problems in physics; as a matter of fact, the problem of cosmological constant actually becomes an inescapable fundamental puzzle in physics.

The long-term perplexing problem of cosmological constant has been completely solved by proving that the so-called problem in itself is mechanistically thus essentially invalid (P. 788 ~ 789, 7.7.2, Ch.7B, reference #2). Why? All in all, the concept of cosmological constant has been proven to be mechanistically thus essentially wrong, because the cosmological constant is literally the aftermath of the mechanistically thus essentially wrong postulate of ‘invariant scales of space (length) and time’ embedded in Einstein’s postulate-based general relativity (EPBGR). [*Note, EPBGR’s postulate of ‘invariant scales of space (length) and time’ has been proven to be mechanistically thus essentially wrong (P. 420 ~ 423, 4.5.2, Ch.4A, reference #1)].

The key to understanding of this solving the problem of cosmological constant: (1) the well-known and undeniable fact, which is that Einstein’s postulate-based general relativity (EPBGR) does not and cannot solve the problem of why space and time are variable thus relative in gravitational field. (2) The so-called cosmological constant turns out (proven) to be literally the consequence of EPBGR does not and cannot know why time and space are variable thus relative in gravitational field (i.e., the root of the cosmological constant is that EPBGR does not and cannot know why space and time are variable thus relative in gravitational field). (3) The cosmological constant is embedded in EPBGR, whereas EPBGR has been proven to be mechanistically thus essentially wrong literally due to it utterly skipping over the mechanism thus essence behind its describing phenomena via the “help” of a series of postulates and assumptions (P. 399 ~ 444, Ch.4A, reference #1). (4) The cosmological constant is connected to ‘expanding Universe’ (i.e., the zero value of cosmological constant corresponds to ‘expanding Universe’), whereas the ‘expanding Universe’ has been proven to be mechanistically thus essentially wrong (P. 761 ~ 765, 7.2, Ch.7A, reference #2). (5) The cosmological constant is connected to the hypothesized dark energy that has been proven not existing at all (P. 784, 7.6.3, Ch.7B, reference #2). (6) Knowing of why time and space are variable thus relative in the Universe (P. 445 ~ 514, Ch.4B; P. 541 ~ 548, 5.5, Ch.5B, reference #1). (7) Knowing of the newly revealed mechanism of universal gravitational constant G – the value of G is and represents the reduction in the scales of space and time occurring in gravitational field (P. 505 ~ 509, 4.16, Ch.4B, reference #1).

Reference #1: 2009, Bingcheng Zhao, From Postulate-Based Modern Physics to Mechanism-Revealed Physics [Vol. 1(1/2)], ISBN: 978-1-4357-4913-9. Reference #2: 2009, Bingcheng Zhao, From Postulate-Based Modern Physics to Mechanism-Revealed Physics [Vol. 2(2/2)], ISBN: 978-1-4357-5033-3.

Ph.D., Bingcheng Zhao, The author of “From Postulate-Based Modern Physics to Mechanism-Revealed Physics” 1401 NE Merman Dr. Apt. 703, Pullman, WA 99163  USA. Email: bczhao12@gmail.com  or   bzhao34@yahoo.com   or   bingcheng.zhao@gmail.com  —Preceding unsigned comment added by 204.52.246.120 (talk) 19:17, 18 March 2010 (UTC)


 * Wikipedia is not the place to try to publish or popularize your own ideas. See WP:NOR and WP:RS. --Christopher Thomas (talk) 19:21, 18 March 2010 (UTC)

History has no dates
I would hope to find when Einstein added and removed the cosmological constant. Was it in the 1916 paper? That sort of thing. The History section has no dates at all. Ronstew (talk) 19:25, 6 December 2010 (UTC)
 * I think it was always there in his work - his "mistake" was that he didn't remove it. -- cheers, Michael C. Price talk 15:53, 25 August 2011 (UTC)

Positive value
I removed the " or even 10−120 in reduced Planck units." because "reduced Planck units" is not a unit. It is like saying the CC has the value of 10^-35 in SI units. And it causes confusion with the next paragraph which states "As noted above, the measured cosmological constant is smaller than this by a factor of 10−120." But it is NOT mentioned above. — Preceding unsigned comment added by 217.225.77.88 (talk) 03:15, 25 August 2011 (UTC)

It is curious that the powers being described in this section (...Multiplied by other constants that appear in the equations, it is often expressed as 10−35 s−2, 10−47 GeV4, 10−29 g/cm3.[8]....) look like negative powers of numbers related to the Golden Ratio, that is, 29 and 47 are successive Lucas number, and 35 is close to 34, Fibonacci. I realize that the units are arbitrary, so the coincidence is very amusing. If the numbers were all based on something more fundamental... oh, well... 67.81.236.32 (talk) 00:58, 20 February 2012 (UTC)

Hierarchy problem and Cosmological constant problem
Can someone please help me spell out the common source of both Hierarchy problem and Cosmological constant problem? I seem to see a clear connection here.Mastertek (talk) 08:52, 5 December 2011 (UTC)


 * The short version is, they aren't related.


 * The cosmological constant is expected to be due to vacuum energy or similar processes. Calculating what the zero-point energy of vacuum should be is a tricky process, and calculations so far don't match observations. The hierarchy problem is the observation that a mathematical tool called renormalization, used for applying certain types of field theory, only produces "nice-looking" results if certain suspicious coincidences occur when setting up the theory it's being applied to. Two very different artifacts in two very different situations. --Christopher Thomas (talk) 09:39, 5 December 2011 (UTC)
 * @Christopher Thomas yes, however this classic claim is misleading and wrong: vacuum energy density is quantum and the cosmological constant is classical. Even the semi classical formulation is ill grounded, since the expectation of the vacuum fluctuations is not observable. So, it's just a "false issue" aimed at best at showing how gravity is not similar to the other forces (since it is sensitive to absolute energy levels). 2A01:E0A:159:17E0:40AF:4749:EF7C:A1E6 (talk) 21:41, 21 September 2023 (UTC)

Removal of section on de Sitter relativity
The section was of negligible relevance to the main subject of this article. The short text also contained a factually wrong statement, even contradicting the main article on de Sitter relativity. It did not even contain any references for its claims. Const.S (talk) 20:28, 8 December 2011 (UTC)


 * Agreed WP:Undue D. Flassig (talk) 21:27, 8 December 2011 (UTC)

CC value based on quantum field theory
It's said "measured cosmological constant is smaller than this by a factor of 10^−120." Does this means "1"???Mastertek (talk) 14:23, 19 March 2012 (UTC)

Lacks definition in opening paragraph
This "explanation" lacks an explanation of what the cosmo constant is in the opening paragraph. That paragraph notes its historical significance but fails to provide a useable definition. Please add a definition of what the cosmo constant is. And please don't fall back on some tired cliche about how it's all in the math. Lets have a comprehendible definition, preferably one which can be maintained in the mind after the page is exited. — Preceding unsigned comment added by 70.112.237.119 (talk) 02:46, 19 April 2012 (UTC)


 * I agree; this page doesn't actually give any values for the constant, or even an expression! So frustrating when trying to work on Cosmology HW.

Popa910 (talk) 03:38, 19 October 2015 (UTC)

Can some expert here establish in the article the relationship between Λ and the Hubble constant?
As best as I can tell, Λ is the square of the Hubble constant. Λ has dimension of T-2 and the Hubble constant has dimension T-1. In Planck units, Λ has a value of about 10-122 and the Hubble constant has value of 10-61. Given that the values are not known precisely, I find this to be just too coincidental, but I am not sure from what data the values are derived from and how they are derived. I find it hard to believe that they are derived independently from observed data.

Can some cosmologist comment on this? 71.169.189.151 (talk) 18:00, 28 August 2012 (UTC)


 * Have you looked at the article for Hubble's Law? It shows how the Hubble parameter is derived and measured. The cosmological constant was invented by Einstein to initially solve a problem of 'world particle' pressure - it wasn't necessarily derived originally. Of course, just because you don't believe it could be true doesn't mean that it isn't. AstroCog (talk) 18:21, 28 August 2012 (UTC)


 * Of course I have looked at Hubble's law. It mentions cosmic microwave background radiation and Lambda-CDM model which are also referred to here.  It also show a graph with some points regarding redshift velocities with a slope of 68 km/(s Mpc) which I believe was the original believed value.  But I am not a cosmologist or astrophysicist.  I cannot tell how the value of Λ is determined from observational data.  I cannot tell whether or not there is a common root to the data for how the actual numerical values are determined.  That's why I am asking people more knowledgeable than myself. I do understand flaws in argument such as Argument from lack of imagination but I don't know enough about the mathematical specifics for how these values are extracted out of astronomical data and what astronomical data is used to know whether or not they are related even though it's easy to imagine that they are, given their dimension and values.
 * So I take it that your expert answer is "No, the two astronomical parameters have nothing to do with each other." 71.169.189.151 (talk) 19:13, 28 August 2012 (UTC)
 * I linked to argument from incredulity - WP unfortunately calls it argument from lack of imagination as well. Anyway, Λ is currently invoked for both inflationary time periods of the Universe - this part isn't measurable directly - and also for the observed accelerated expansion. I'm sure there are cosmologists who use it in theoretical models as well - different values can give you different outcomes for the Universe. H naught, as I understand it, is the local rate of expansion. Calling it a "constant" is a bit of a misnomer, because astronomers are able to determine velocities and distances for galaxies much further away than Hubble was able to do. So today, we measure a "steep" slope to the Hubble plot for "local" distances that are within a few million light-years. For galaxies we observe very far away (I'll say 10+ million light-years distant), we measure a lower slope for the Hubble plot, which means that over time, the expansion rate has increased. In order to keep the field equations of general relativity consistent with this observational result, there has to be now a value for Λ to account for the accelerated expansion. That's how astronomers arrive at the value observationally. I'm not sure about any deeper connection between the two values...sorry. AstroCog (talk) 20:58, 28 August 2012 (UTC)


 * You're asking about a numerical coincidence when H and Λ are expressed in Planck units, and whether there's a deep reason why it should be the case. It's an interesting question, and I think you will get some good answers if you ask at the science reference desk.  --Amble (talk) 19:50, 28 August 2012 (UTC)


 * This fact follows from the Friedmann equation, which gives the critical density $$ \rho_{crit} = 3 H_0^2 / 8 \pi G $$ (in mass density units), and the observational estimate that the dark energy contributes close to 73 percent of that in the concordance model. So, this is essentially the same as the coincidence problem; note that if the cosmological constant were 100x bigger (and all other early-universe physics were unchanged) then H would be ~ 10x bigger "now", but the universe would have gone into exponential expansion long ago, no galaxies would have formed and we would not be here; while if the cosmological constant were 100x smaller, we would not have noticed it as positive by "now".

Wjs64 (talk) 22:48, 29 August 2012 (UTC)

Einstein's "biggest blunder"
See "Einstein Likely Never Said One of His Most Oft-Quoted Phrases" for research challenging Gamow's assertion (which is repeated in a number of other WP articles); the statement apparently needs to be qualified. Suggestions? 209.6.114.98 (talk) 21:50, 9 August 2013 (UTC)
 * Livio's book (mentioned in the "Einstein Likely ..." article) has as Chapter 10 "The 'Biggest Blunder'", beginning on p. 221 and concerning Einstein's lambda (or cosmological constant). The third section of the chapter, "What's in a Word?", concerns the "blunder" phrase itself and encompasses pp. 229-243. (The 4th and last section of the chapter puts lambda into the context of research after A.E.'s death.)  Livio says that thoro research found no evidence attributing the blunder phrase to AE, except a seldom-cited article and the autobio, both by Gamov, published respectively about 17 months and about 25 years after AE's death. He also quotes a 1986 article by the naval officer who had recruited both AE and Gamov as wartime R&D consultants:
 * Gamov, in later years, gave the impression that he was the Navy's liaison with Einstein, that he visited every two weeks, and the professor "listened" but made no contribution -- all false. The greatest frequency of visits was mine, and that was about every two months.
 * IMO, Livio's evidence (which extends beyond what i've just cited) suggests that Gamow -- perhaps motivated by jealousy of Einstein's reputation and disappointment over disproof of his own (really cool!) continuous-creation alternative to the Big Bang theory -- is an unreliable and unsupported witness for the "blunder" quote, and of course YMMV. (IMO Gamov may have been inspired (if it was published in time) by what is documented in Linus Pauling's appointment book, namely AE's 1954 statement, that his "one great mistake" -- even tho he thot "there was some justification" -- was urging FDR to build nuclear weapons.)  More to the point, i think we should report in the article that Gamow wrote twice, after AE's death, that he said the cosmological constant was his biggest blunder, and that Livio has assembled what he considers reasons for doubting it.   BTW & FWIW, on p. 233 Livio quotes Gamow's 1970 bio:
 * ... this "blunder", rejected by Einstein ....
 * (which contrasts with the indirect quotation in the 1956 article) and comments
 * The use of quotation marks around the word "blunder" seems at least to suggest that Gamow meant to imply an authentic quote.
 * (as opposed to a total paraphrase) but he doesn't draw any inference from the absence of quotations marks in the corresponding wording of the article that preceded the bio. --Jerzy•t 06:33, 19 February 2014 (UTC)
 * The "never said" article cited in the first contrib in this talk section includes a confusing image that also appears (monochrome) on p. 234 of Livio's book, and Livio's text references the image in the 'graph that includes the middle of p. 233. It's handwritten on a printing-press "week-at-a-glance"-style appointment-book page for [the last week that began in] "August, 1956", but a long handwritten entry begins "My visit to Einstein on 16 Nov. 1954" then continues "(See notes written by me a few minutes after the meeting -- beginning of 1954 diary)" (It must be read with care, as it is written around unrelated short entries for "Sun. 26", and extends all the way into the space allocated for "Fri. 31".)  I read online a similar image, presumably from Pauling's 1954 appointment book; i inferred that he transcribed in fall of 1956 much of what he presumably wrote "[standing? sitting?] on the sidewalk" a few minutes after leaving Einstein in 1954, perhaps with a slight change in the text.  I inferred that Pauling transcribed from the old book to the then current one so he could leave the original in his files but consult the text at another location from the new one with current notes and appointments. (It's late, and i am saving this much before poking around and hopefully adding a link to the '54 image.) (Oh, not so hard as i feared!)  Narrative (and unusable image) abt Russell & Pauling, and Einstein's last months and images and text re the '54 diary entry. Pauling added ( in '56 ) part of a point from the discussion that he knew ( in '54 ) he would recall without any need to write it down that day in '54. --Jerzy•t 07:39, 08:17 , 08:47, & 09:04, 19 February 2014 (UTC)


 * There is another excellent discussion on this topic at http://delorian64.wordpress.com/2013/08/10/did-einstein-ever-say-biggest-blunder/. It confirms much of what is said here, but also notes the possibility that Einstein said something in German to Gamow, which then Gamow translated as a direct quote.  Either way, AE clearly later rejected the cosmological constant.  The article also has a great quote from Einstein replying to Lemaitre on this issue, where he says that "introduction of such a constant appears to me, from the theoretical standpoint, at present unjustified."  Al&#39;Beroya (talk) 09:05, 14 July 2014 (UTC)

Unclear article
The introduction doesn't state what the cosmolocical constant is. Is it defined as the rate of change of acceleration due to dark energy with respect to position expressed in s-2? Is it that quantity ÷ c2 as in § Positive value? Is the critical density defined as what uniform density of matter in the universe would have gravity exactly cancel out the cosmological constant, i.e. is the critical density $Λ⁄4π⁄3G$? Is vacuum energy defined to be critical density × c2? It will not do having this article define the cosmological constant in terms of critical density but also have critical density define critical density in terms of the cosmolocigcal constant because some people might not know what either of them mean and when they're reading an article about one, be unable to click the link to the other article to learn what the other one means. Blackbombchu (talk) 03:52, 13 March 2014 (UTC)


 * The main problem is that modern reinterpretation as vacuum energy density (which is largely responsible for the invention of "dark matter" and "dark energy") has obscured the original usage. For Einstein, the CC was merely a small, dimensionless constant that caused the vacuum general-relativistic field equations to form a compact universe instead of an unbounded universe.  The connection of the CC with a pervasive nonemptiness of the vacuum is a later, somewhat quantum-inspired, development.
 * No amount of gravity can "cancel" the CC; according to the background-vacuum model, energy from some form of gravtitating matter is required to give the CC a non-zero value. The problem the dark-matter proponents think they are addressing is that the amount of cosmic matter we are able to observe is insufficient to give the CC anywhere near the value computed from models of expansion of the universe.  Of course the models are very likely wrong, but workers in the field don't like to contemplate that.  — DAGwyn (talk) 12:18, 5 August 2015 (UTC)

Cosmological constant linked to the quantum potential
The Arxiv paper Spontaneous creation of the universe from nothing has received some press reports and links the cosmological constant with the quantum potential and maybe with the initial exponential expansion of the baby universe (if I understand what it says). How do we decide whether the paper should be mentioned in the article? Absinthia Stacy (talk) 15:37, 15 April 2014 (UTC)

Dark energy primary requirements
From the introduction to the article, "...the main required properties of dark energy are that it dilutes much more slowly than matter as the Universe expands, and that it clusters much more weakly than matter, or perhaps not at all." Does this leave out it's main required property? Shouldn't this read: "...the main required properties of dark energy are that *it functions as a type of anti-gravity,* that it dilutes much more slowly than matter as the Universe expands, and that it clusters much more weakly than matter, or perhaps not at all." Bob Enyart, Denver KGOV radio host (talk) 17:08, 3 March 2015 (UTC)
 * Any objection to incorporating this into the main article? Bob Enyart, Denver KGOV radio host (talk) 22:59, 17 April 2015 (UTC)

Seeing no objections, I went ahead and made this edit. Thanks! Bob Enyart, Denver KGOV radio host (talk) 12:13, 26 April 2015 (UTC)

Can someone please put appropriate units on this thing?
So "ΩΛ is estimated to be 0.692 ± 0.010 ..." 0.692 what?

Please someone knowledgeable express this in units so that people reading this can understand what the scale of ΩΛ is. 166.184.170.35 (talk) 21:13, 20 March 2015 (UTC)


 * Like, make something up just to please you? The constant is a dimensionless value, which the article clearly specifies. The lack of units is appropriate. Owen&times;  &#9742;  23:23, 20 March 2015 (UTC)

I propose the following changes
I have written very slowly write very slowly these suggestions and their form is reasonably definitive. I would like to know if someone else feels them useful.

- start

In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is defined through the energy density of the vacuum by Λ = 8π (G/c2)ρvac and has the same dimensions of the scalar curvature (reciprocal square length). Some authors, however, define Λ as c2 times this quantity and it is also common to quote the energy density directly, though still using the name "cosmological constant" for it.


 * I witnessed the following event: a reader needing only a coarse definition (in the event a school teacher) has understood from the summary that the CC is the energy density and has skipped the technical section (declared hard), so propagating the sloppy definition as an exact one.


 * I feel that a few lines in the equation section may be dropped after this change.

equation where $$R_{\mu \nu}\,$$ is the Ricci curvature tensor, $$g_{\mu \nu}\,$$ is the metric tensor, $$\Lambda\,$$ is the cosmological constant, $$G\, $$ is Newton's gravitational constant, $$c\,$$ is the speed of light in vacuum, $$R\,$$ is the scalar curvature and $$T_{\mu \nu}\,$$ is the stress–energy tensor. $$R$$ should not be confused with the scale factor $$R(t)$$ appearing in the Friedmann-Lemaître-Robertson-Walker metric. When Λ is zero, this reduces to the original field equation of general relativity. When T is zero, the field equation describes empty space (the vacuum).


 * I have largely taken this from the EFE article. I feel this an ecxcellent compromise between self-completeness and shortness.

value, related quantities and conventions

The present observational data allow only to estimate the magnitude order of the cosmological constant, that corresponds to the upper limit for the absolute value allowed by the data available until the late 1990s (i.e. before the discovery of the accelerating expansion) Λ ≈ 10−52m−2 ≈ 10−122 (c3/Għ) &nbsp &nbsp Λ c2 ≈ 10−35 s2   ≈ 10−122 (c5/Għ) where the last member gives the value in natural (Planck) units. Some authors define as cosmological constant the quantity Λ c2 and use the symbol Λ for it. Derived quantities are (1/8π) Λc2/G ≈ (1/25) 10-25 kg/m3 ≈ (1/25) 100 amu/m3 ≈ (1/25) 10-6 solar mass / parsec 3 (1/8π) Λc4/G ≈ (1/25) 10   nJ/m3 = (1/25) 10-8 Pa that are respectively the associated mass densities and energy. This last is and an order-of-magnitude estimate of the associated pressure, which depends on the model). The literature often employs the convention c=ħ=1. Setting c=1 does not simply give unit numerical value to the light speed, but also gives the same dimensions to space and time, so that the second becomes a length unit equal to 300000 km. Under this convention the two definitions of the cosmological constant are identical. Also mass and energy have the same dimension and the joule becomes a mass unit equal to 1.1 10 -17 kg (the numeric coefficient is the SI value of 1/c2). Setting then ħ=1 gives to the energy the dimension of a reciprocal length, so that the joule corresponds to 3 1025 reciprocal meters and Λ/G = (Λ/G) cj ħk ≈ 10-84 J4 ≈ 10-47 GeV4 ≈ 1017 m-4 whatever j and k are (all these quantities have the same value 10-122 in Planck units). In the SI, the J4 value corresponds to j=7 and k=3 and the m-4 to j=3 and k=-1.


 * this might be added at the end of the section positive value
 * I remember that in the 1980s the Planck units were most often defined with h=1, so reduced P.U. denoted those with h-bar=1


 * The text should state clearly, "The cosmological constant, in its original form, has the same units as scalar curvature, e.g. meters−2 in the metric system." I think any discussion of units beyond that would just confuse most readers.  — DAGwyn (talk) 05:49, 7 August 2015 (UTC)
 * I agree pietro I have accordingly modified the proposed new start 93.145.250.148 (talk) 17:07, 28 August 2015 (UTC)

physical consequences

The physical effect of the lambda term is most evident in the equations for the scale factor R(t) of the Robertson-Walker metric, that is proportional to the radius of the universe


 * $$\left(\frac{\dot R}{R}\right)^{2} + \frac{kc^{2}}{R^2} - \frac{\Lambda c^{2}}{3} = \frac{8\pi G}{3}\rho$$
 * $$2\frac{\ddot R}{R} + \left(\frac{\dot R}{R}\right)^{2} + \frac{kc^{2}}{R^2} - \Lambda c^{2} = -\frac{8\pi G}{c^{2}} p.$$

which shows that a positive value of Λ accelerates the expansioof the universe. The same conclusion is seen from the classical limit of the equation for the gravitational potential

\nabla ^2(V) + \Lambda c^{2} = 4\pi G \rho

which implies that an observer in the origin sees an additional force
 * $$ \vec F=(mc^2 \Lambda/3) \vec r $$

upon a particle located at $$\vec r.$$


 * I do not know the exact place where insert this. A good place seems the end of the equation paragraph. This info comes from A. Harvey and E. Schucking; Einstein's mistake and the cosmological constant, Am. J. Phys. 68, 723 (2000)


 * as already pointed out by ather talkers, the CC is "fully consistent with the equations of the general relativity because it is effectively an integration constant" (Rowan-Robinson, Cosmology, Clarendon 1977, pag 123); it would be interesting to know the integral. It was set to zero to have the theory as simple as simple as possible

Assessment comment
Substituted at 12:19, 29 April 2016 (UTC)

Cyclic model: what?
"Instead, the cosmological constant gradually diminishes over many cycles to the small value observed today."

Then that's some other model of "dark energy". The point of the cosmological constant model of dark energy is that it's ... constant ... right?

I looked at the arXiv link in the primary source cited, it seems to use a scalar field, and not use the term "cosmological constant". That seems right.

Perhaps this should be moved to a "dark energy" article. --174.116.141.16 (talk) 19:11, 5 July 2016 (UTC)


 * Done. --174.116.141.16 (talk) 23:38, 28 August 2016 (UTC)

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A whole lot of talk
It is mentioned in the article that "space" has density (kg/m3) and that this density can vary across the space. Then why-o-why, there is still talk of "curvature" of space in every astrophysics class, if all you need is for the gravity to compress the space (increase its density, because gravity attracts mass) and you get exactly the same effect as with curvature?
 * Energy density &#9798; CUSH &#9798;

please check
I feel that in

The cosmological constant has the same effect as an intrinsic energy density of the vacuum, ρvac (and an associated pressure). In this context, it is commonly moved onto the right-hand side of the equation, and defined with a proportionality factor of 8π: Λ = 8πρvac, where unit conventions of general relativity are used (otherwise factors of G and c would also appear, i.e. Λ = 8π(G/c2)ρvac = κρvac, where κ is Einstein's constant). It is common to quote values of energy density directly, though still using the name "cosmological constant", with convention 8πG = 1. The true dimension of Λ is a length−2.

should appear

Λ = 8π(G/c4)ρvac = κρvac,

because otherwise this rho is dimensionally a matter density. I note that


 * this misprint seems related to the fact that some authors use lambda for lambda*c^2 -- it might be useful to warn the reader of this occurrenc
 * in the section positive value the energy density of vacuum appears explicitly as a mass density (there are also problems with MKSA and cgs values).

I would also enjoy something like

(and an associated pressure) -> (and associated pressure P=constant*rho)

with a guess of the constant (that I suppose to depend on the details of the theory, a fact that makes this addition difficult)

If you are expert in this, I suggest to give in the proper article a clear definition of the Gibbons-Hawking temperature. This because I have found in many places the definition T=H/2pi in natural units, from which I have deduced T=hbar*H/2pi*k. Unfortunately, the value 10(-29) comes out with T=hbar*H/k.

pietro (by the way, I wrote talk 29 and if you feel that some consideration I made there may be useful, I may revise for an insertion) 151.29.203.130 (talk) 08:30, 21 February 2018 (UTC)

Questionable claim regarding values of energy density
In the Equation section, the following statement currently appears without citation "It is common to quote values of energy density directly, though still using the name "cosmological constant", using Planck units so that 8 π G = 1 ."

Is this actually common? My understanding (per the relevant Wikipedia entry) is that, using Planck units, G = 1, so it would follow that 8 π G = 8 π. Furthermore, I have not been able to find another instance where this claim is made (let alone justified).

Recommend that a citation for this be provided, if indeed it's true, or that the claim be deleted/clarified if not. WJTP (talk) 03:17, 2 February 2021 (UTC)

A Perturbation Expansion of the EFE
Cornwall is suggesting, in provisional research released on preprint servers, that an expansion of the Einstein Field Equations to the 2nd order in the Stress-Energy Tensor (and 3rd order in the Einstein/Newton constant) is the way to solve the Cosmological Constant problem (Cornwall does consider the Pauli theory on attempted cancellation of Bosonic and Fermionic contributions and notes that this cannot be done). His rationale is that zeropoint energy is a fluctuation at zero particle count (it has a variance but no average) and so it shouldn't properly be included at zeroth order in the SET. It is properly included at 2nd order in a Taylor Expansion of the SET in frequency, where (Δω)2 makes sense in describing the fluctuation by its variance. Interestingly what results is some 10-9 times down on the Cosmological Constant (10-9 J/m3) as compared to the currently accepted magnitude of the Zeropoint (some 10120 J/m3), so Cornwall suggests that there is interaction energy between the modes of the zeropoint to make it some 109 times bigger (i.e. 10129 J/m3) in a reasonable model (the electric fields of fluctuation of the modes must interact with one another). He has left a comment (on vixra) that he believe that the radiation damping in the model may fix and limit increase at around 109 and may have something to do with the fine structure constant, which describes the coupling in Electromagnetic theory. It is of note that it is extremely sensitive to this parameter and may explain Cosmic Inflation, if it varied in the past.

Inaccuracy in introduction
The cosmological constant is not "the energy density of space, or vacuum energy, that arises in Albert Einstein's field equations of general relativity." There is one theory, part of quantum mechanics, not general relativity, that gives rise to a cosmological constant. It has nothing to do with Einstein. The original cosmological constant was an arbitrary term added by Einstein. It was not generated by vacuum energy. Many, many years later the idea of vacuum energy combined with the discovery of increasing universal expansion to regenerate interest in the cosmological constant with a currently unproved hypothesis about what might generate it, namely vacuum energy. The introduction totally fails to convey most of this factual information. I will rewrite it if someone doesn't do a better job first. Zaslav (talk) 21:34, 28 August 2021 (UTC)

Lead graphic conveys misleading expansion rate
The lead graphic is a misleading introductory visualisation of universe expansion. Please see my critique here; https://commons.wikimedia.org/w/index.php?title=File_talk:CMB_Timeline300_no_WMAP.jpg#Graphical_representation_of_the_expansion_of_the_universe Richardbrucebaxter (talk) 00:56, 7 September 2022 (UTC)

Sign convention
Isn't it the case that the sign of the cosmological constant depends upon the sign convention of the metric tensor? If so, which convention is this article assuming: $gμν ~ (+, −, −, −)$ vs. $gμν ~ (−, +, +, +)$ — Q uantling (talk &#124; contribs) 22:54, 10 November 2022 (UTC)

cosmological coupling?
Looks like we might now need an article on the topic of "cosmological coupling". AllGloryToTheHypnotoad (talk) 14:11, 16 February 2023 (UTC)

Wtf is this non-sense ?
The article says Friddman worked with the original general relativity equations. But the cosmological constant also appears in Friddman's equations ! Also, you need to explain why Einstein removed the cosmological constant, if Fridmann used it in his equations that gave an epxanding universe. By removing it would simply revert to a contracting universe, and not 'update' his theory to an expanding universe. Marvas85 (talk) 01:49, 8 September 2023 (UTC)

The final section of the article is a logical fallacy and should be deleted together with its footnote reference articles
The final sentence reads:

It is also possible that the difficulty in detecting dark energy is due to the fact that the cosmological constant describes an existing, known interaction (e.g. electromagnetic field).[37]

Physicists are looking for dark energy. They're not looking for a cosmological constant, which is a number describing the cause and effect dark energy is believed to have. And so far they've been unable to find the dark energy. It's quite possible the cosmological constant is an inaccurate description of the effects caused by dark energy, i.e., we've modeled dark energy incorrectly. In that case the model is wrong. That in itself is no reason for thinking that the model accurately models something other than dark energy. And even if it - which is highly unlikely - then presumably we would have found that other thing which it models and confirmed that it models something other than what we thought it modeled. But even in that highly unlikely scenario, that would not explain why we had not found dark energy. The cosmological constant does not define or constrain the experiments conducted to search for dark energy. So it doesn't explain our failure to find it. The entire last paragraph makes no sense under any possible scenario. Only if the cosmological constant defines the search criteria can it be suggested as a reason for failure of the search to find anything. TopScholarNZHistory1993 (talk) 21:21, 21 October 2023 (UTC)