Talk:Lambda-CDM model

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Older comments[edit]

"This component makes up 26% of the energy density of the present universe. The remaining 4%"

I'm not qualified to fix it, but that sure looks wrong to me...


70% are alrady accounted for (Lambda) in the preceding paragraph. --Pjacobi 17:48, 2005 May 4 (UTC)

The latest results from the WMAP probe have estimated these numbers to be, indeed, 74% Dark Energy, 22% Dark Matter, and (still) 4% normal matter. -- 04:57, 5 June 2006 (UTC)


I didn't understand your edits to ΛCDM. It really says nothing about the finiteness of the universe, other than that it is substantially larger than the observable horizon. Can you please discuss on the article's talk page? Thanks –Joke137 19:59, 16 Jun 2005 (UTC)

It is the simplest model that is in agreement with all the observations, apart from the subjective debate concerning whether or not an infinite Universe is simpler than a finite Universe. The model is not a complete model, because it is only local and, if interpreted literally, represents the Universe to be infinite in spatial volume.

The ΛCDM is a Friedmann-Lemaître-Robertson-Walker model. It is a scientific model which assumes that general relativity is correct. If we ignore topology (hmmm we should probably add this as an implicit assumption to the article content), then a flat or hyperbolic model is infinite, and a spherical model is finite, in spatial volume. See shape of the universe for more about possible shapes of a spatial section at constant time in this model.

The ΛCDM model, if interpreted naively (literally) very definitely represents the Universe to be infinite. No serious scientist really tries to overtly claim that the Universe is necessarily infinite, but we agree that it's a property of the model. Please read wikipedia pages on cosmology or any introductory cosmology text on the web or in print.

These are the simplest assumptions for a consistent, physical, local model of cosmology. However, ΛCDM is a model, and it is only a local model.

general relativity is a local theory. It is about the limit (mathematics) towards a point. ΛCDM is fundamentally local, especially in the way stated in which it says nothing about global properties. It makes no claim at all to be a global model. The inflationary extrapolation says that the ΛCDM model concerns just one extremely tiny sphere of space-time, whose radius is the particle horizon, outside of which we have (virtually) no information.

i can explain more if this is unclear. To me this is a very sensitive point, because IMHO it's extremely unfair of scientists to give the false impression that we have a scientific model of everything when really we only have a scientific model out as far as we can go in any objective sense.

BTW, it still remains possible that the ΛCDM model + topology just possibly might be the correct model of the whole Universe and there a bunch of us working on this - see for (limited info on) our most recent conference, but that's independent of the ΛCDM article.

Please put back my corrections, or else ask for more explanations. Certainly i could be wrong (my ability to make errors has been proven beyond the faintest doubt ;), but i would be surprised to be wrong on this particular issue. Boud 11:38, 17 Jun 2005 (UTC)

The size of the universe is a metaphysical problem at best. OTOH the size of our local patch is finite for an universe which is asymptotically de Sitter. No signal from beyond will reach us nor can we signal to any point beyond our patch, provided Einstein locality holds. --Pjacobi 11:52, 2005 Jun 17 (UTC)
Wrong about the first sentence. If the Universe is much larger than the horizon, then the size of the Universe is a metaphysical problem. Certainly, this is a reasonable possibility given present observations, but it is wrong to state at best. However, even if the size of the Universe is a metaphysical problem, it is part of the model. The model is a methematically described model. It is called the Friedmann-Lemaître-Robertson-Walker model and naively or literally interpreted, it is a model for the entire Universe. In this sense, using your terminology, the FLRW class of models are in many cases very metaphysical. We cannot have this both ways. Boud 13:41, 17 Jun 2005 (UTC)
OK, finding an observable "edge of the universe" would make the size question a valid question of physics. And tests, whether there is a wraparound in observable distances have been done.
But whether we should give any signifance to the fact, that the model describes something outside the local patch, isn't that clear to me.
Pjacobi 14:10, 2005 Jun 17 (UTC)
Our obligation to the reader of an encyclopaedia page is to make it clear, correct and avoid misleading the reader. If we fail to mention the fact that the model (interpreted literally - and after all, it is a 'mathematical model, it's not just poetry) describes something outside of the local patch, then we are misleading the reader. If we fail to say that the model is incomplete, we are also misleading the reader. If we suggest that an infinite model is simple, we also mislead the reader (e.g. in a truly infinite universe, the probability of another wikipedia being written somewhere else in the Universe, at some time, with exactly the same sequence of editing steps as here on Earth, except that every occurrence of the word Universe is replaced by pink elephants, is unity: infinity is not simple). Boud 14:55, 17 Jun 2005 (UTC)
You have stated a common misunderstanding about the nature of infinity. Infinite space does not guarantee that all concievable events will occur. Only events which have non-zero probability per unit space are guaranteed to occur. By analogy, consider the real number interval [0,1]. Now pick a number on that interval. Since there are an infinite number of choices, the probability of you picking any particular number is exactly 0, and yet, I am sure you managed to pick one. (Was it 0.2351532?) Furthermore, since the real numbers are uncountable, even if you continued to pick numbers at random for an infinitely long time, there would still be numbers that you would never manage to pick. It is the same thing with the universe. Even if it is infinite in extent, there can still be possible sequences of events which will never happen to occur, and just because something has happened once is no guarantee that it will ever happen again anywhere else in the universe. In other words, just because you picked the number 0.7345312 today does not mean you would ever pick that number again even if you went on picking at random forever. So, in short, you are right, infinity is most definitely not simple, but I wouldn't hold out for the pink elephants. Dragons flight 00:16, Jun 18, 2005 (UTC)

I really don't know what to make of this. ΛCDM is a model used to compute, among other things, big bang nucleosynthesis, the cosmic microwave background radiation and the spectrum of the large-scale structure of the cosmos. Any model, so far as I know, that is in clear quantitative agreement with these data is based on general relativity (or very simular theories) and assume a perturbed Friedmann-Lemaître-Robertson-Walker background. ΛCDM happens to be the simplest, because, in addition to fundamental physics parameters, it adds only six parameters to the model. It does this by choosing special values for the others, where it is possible (i.e. a cosmological constant, dark matter has vanishing thermal pressure, etc...). One such choice is that the size of the observable universe is much larger than the particle horizon.

I really don't understand this point about a local model. The only people I know of advocating for a non-local model of physics are the holographic principle people. –Joke137 15:03, 17 Jun 2005 (UTC)

I made another edit. Is this satisfactory? The main point I want to make is that the ΛCDM model is more a physics-inspired mathematical model than a complete physical theory. –Joke137 15:23, 17 Jun 2005 (UTC)

i find the comments by "Boud" incomprehensible. general relativity is the standard accepted account for gravitation, and explains gravitational/energy (luminosity) observations of very distant stars and galaxies. all scientific cosmological models are based on the cosmological principle, the assumption that we occupy no special location in space and that space looks pretty much the same in all directions, on a large enough scale. (the &Lambda'CDM cosmology does vary with time.) "out as far as we can go" is an issue of observation or of the sensitivity of measurements, which are continually improving, and all vastly improved observations continue to validate the cosmological principle. at the same time, observational limits are not a "metaphysical problem" *within* the universe, and there is nothing *outside* the universe that has to do with science. the issue of "finiteness" concerns the geometry or curvature of the universe, not its metaphysical status. all we can say at present is that the universe appears to be very close to flat or, if it is curved, that we do not have (across roughly 60 billion light years) a wide enough view to clearly observe the curvature in effect. for example, the curvature is known to be less than the curvature necessary to "magnify" the apparent size of anisotropies in the cosmic microwave background.

i see a clear POV or personal agenda in: "IMHO it's extremely unfair [??] of scientists to give the false impression [?!] that we have a scientific model of everything [!] when really we only [!] have a scientific model out as far as we can go in any objective sense [??]." surprising to find someone who refers to "we" at a cosmology conference (where the name "Boud" does not appear) but traduces scientists as "unfair" and deceptive about "very sensitive" [??] points. i've eliminated the intrusion of metaphysical quibbles in the article and expanded the empirical description. Macevoy (talk) 04:00, 16 December 2009 (UTC)


Not to say I understand the rest of it, but the most mysterious phrase in the article is this: "spatial curvature at the level of one part in ten or one hundred thousand". One hundred thousand what? I can kind of picture spatial curvature of 1/10 as the shape of the top of an umbrella in n dimensions, and it probably corresponds to spatial curvature Ωk = 0.086 at the end of the article. But I can't imagine why that picture would be described with the number 100,000, or any other number unrelated to 1/10. Art LaPella 20:45, September 2, 2005 (UTC)

I may have written that part. Ten or one hundred thousand (Ωk = 10−4 or 10−5) corresponds to the level of spatial curvature predicted by cosmic inflation. It comes from the fact that inflation will have generated fluctuations that are much larger than the particle horizon and these show up as perturbations in the spatial curvature for the universe. The numerical value comes from the 10−5 amplitude of primordial perturbations produced in inflationary models. –Joke137 23:34, 4 September 2005 (UTC)
I think I understand the part I need to. Does that mean you would support this change: " part in ten thousand to one hundred thousand"? Or better, " the level of 10−4 to 10−5" ? Art LaPella 00:04, September 5, 2005 (UTC)

Absolutely. –Joke137 00:11, 5 September 2005 (UTC)

Parameters section values[edit]

Values given in the article do not correspond to values given in WMAP. For example, value for Hubble constant says 69.5 ± 4 here, while in the WMAP it's 71 ± 4. Values for the age of Universe are 13.55 and 13.7 Gyr. Values for Ωb, Ωm, ΩΛ, are also different. Where are they correct? 18:48, 13 September 2005 (UTC)

I strongly assume at both places. In the WMAP article there should be the estimates based on WMAP data alone and here the best concordance estimates (taling into account all data). There are quite lot choices to mix the together (and also to choose which parameters should be estimated an which are fixed), so that there are always some disagreements. --Pjacobi 18:57, 13 September 2005 (UTC)

When I added these values I used the values in the Tegmark et al. 2003 paper, which includes both WMAP and the Sloan Digital Sky Survey. The original WMAP paper included WMAP and 2dF GRS, and got slightly different values. The Tegmark values are better for this page, but hopefully we'll be able to update to WMAP 3yr + SDSS in a few months. –Joke137 03:31, 14 September 2005 (UTC)

I suggest that the parameter values used in the article should be those given here as that is the most complete data set (WMAP 3-year, 2dFGRS, BOOMERanG, ACBAR, CBI, VSA, SDSS, SNLS and SN Gold) at this time and has the smallest errors. 08:40, 20 March 2006 (UTC)

the link cited above has been changed to: ... however the values there are now sourced to a Hinshaw et al. 2008 paper, which i cannot find, and are different from the values in the Hinshaw et al. 2009 paper, which i have used and cited to update the table. apparently both parameter symbols and nomenclature have changed since the wikipedia table was constructed, and i have updated these to match the source table. it also appears clearly from the Komatsu paper that the six parameters used to specify the &LambdaCDM model were *not* the six "basic" parameters that were listed in the table; i've removed the "derived parameters" subhead from the table, listed the parameters to more closely follow the source table, and added some parameters on decoupling. finally, i removed the reference to 2004 data and moved a 2003 reference by spergel as a cite for cosmology. the remaining sources seem badly out of date, but have not been deleted. Macevoy (talk) 16:12, 18 December 2009 (UTC)

The figures given do not add up but come to more than 100%. Please check values or have error bars for the figures. John D. Croft (talk) 14:50, 10 July 2010 (UTC)

Tensor-to-scalar ratio[edit]

This term is not explained adequately, I feel, yet a value is given. Does it relate to the text mentioning gravitational waves?

The abbreviation CMB is used without explanation. I assume it is the initials of Cosmic Microwave Background? 15:19, 27 September 2005 (UTC)

Where to you see "CMB"? Are you reading an old version on a mirror?
Yes, tensor-to-scalar ration should get some explanation, especially as it is not explained in gravitational wave.
Pjacobi 16:24, 27 September 2005 (UTC)
Hmmm, my bad! I can only find "CMB" on the copy of the Non-Standard Cosmology page I saved last night, when Wikipedia was frequently failing to return anything (server problems I guess). And even there I find that it IS properly explained several paragraphs prior, just not linked back.
Yes, please DO explain "Tensor-to-scalar ratio"! Thanks. 07:46, 28 September 2005 (UTC)

Page name[edit]

Should it be at ΛCDM model? Rich Farmbrough 23:30, 11 December 2005 (UTC)

Not without first considering Wikipedia:Naming conventions (use English). Art LaPella 02:48, 12 December 2005 (UTC)
ΛCDM is already a REDIRECT. Should be good enough. --Pjacobi 07:43, 12 December 2005 (UTC)
Should it be "Flat Lambda-CDM model"? If not, then the model should have seven base paramters rather than six, IMO. Spebudmak 06:19, 24 September 2006 (UTC)

No. The ΛCDM model is a minimal model, and has six parameters. –Joke 15:39, 29 September 2006 (UTC)

Well the WMAP papers call it the "Power Law \Lambda CDM" model. I have also seen it called the "Flat Power Law \Lambda CDM" model. I think whether it is "the" minimal model depends on how you define the penalty for adding additional parameters. Take a look at e.g. Table 3 in Spergel 2006. Spebudmak 18:44, 16 November 2006 (UTC)

Pie Chart[edit]

The article gives lambda 74% (or, later, 73.2%), cold dark matter 22% (or, later, 22.2% dark matter), 4% everything else (or, later, 4.4% just baryons), and from the discussion on the talk page and what I've seen elsewhere that sees to be pretty much accurate and up to date. The pie chart gives lambda 70%, dark matter 25%, which disagrees. I realize that these numbers aren't exactly absolutely known to great precision, but I can't see any good reason for the text and the chart to give differing numbers without explanation.

Also, the pie chart breaks out the remaining 5% into four separate components (free H and He, stars, neutrinos, and heavy elements). If this breakdown is accurate, it would be useful to mention it in the text. (Is it accurate? Don't many heavy elements count as part of stars? Doesn't "dark matter" unqualified include free elements and neutrinos, most of the heavy elements, and even many stars (given the standard MACHO definitions)?

As an unrelated side note, there doesn't seem to be any way to find alternative models from this page. (By this, I mean non-flat, topologically complex, fractal, etc. models; not MOND, plasma cosmology, braneworld, or cosmological theories that may or may not predict different models.) -- 09:43, 28 May 2007 (UTC)

I agree, the chart is rubbish, As a rough visual guide it is incorrect (dark matter definitely not represented as 25%), also it occurs in both this article and in the article on dark energy. It'd make sense to have a chart that reflects the proportions in the article and also at least approximates what these look like as a percentage otherwise there's no point having it. Escobar otter (talk) 15:03, 11 March 2008 (UTC)

The pie chart covers up part of the text. Can this be fixed? (talk) 15:44, 22 June 2009 (UTC)

To confuse things further, different wikipedia articles report different ratios while seemingly citing the same source (Gary F Hinshaw et al's 2008 WMAP5 data, albeit with different URLs in the two cases).

The 74/22/4 ratios are also found in the Dark Matter Article.

The Dark Energy article has 3 references to 74%, including: The most recent WMAP observations are consistent with a universe made up of 74% dark energy, 22% dark matter, and 4% ordinary matter.[2]

Note [2] in the above is Hinshaw, Gary F. (April 30th, 2008). "WMAP Cosmological Parameters Model: lcdm+sz+lens Data: wmap5". NASA. Retrieved 2009-05-24.

But the Dark Energy part of the Big Bang article has: Results from the WMAP team in 2008, which combined data from the CMB and other sources, indicate that the universe today is 72% dark energy, 23% dark matter, 4.6% regular matter and less than 1% neutrinos.[27] Note [27] in the above is Hinshaw, G., et al. (2008). "Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results" (PDF). The Astrophysical Journal.

I do not claim enough expertise to resolve this conflict, but having brought it to your attention, hopefully somebody else can. Tlhslobus (talk) 13:05, 9 September 2009 (UTC)

i could find the table, which is referenced to Hinshaw 2008, but the corresponding article appears not to exist (or was only a preprint). the articles i used to update the parameters table were Hinshaw 2009 and Komatsu 2009, linked here: . it seems the WMAP data, combined with Supernova Cosmology Project data and the 2df Galaxy Redshift data, represent a research consensus. but see also ned wright's cosmology pages for an examination of other evidence. —Preceding unsigned comment added by Macevoy (talkcontribs) 19:18, 18 December 2009 (UTC)

The adjective "clickable" in the descrciption of the figure is misleading... (talk) 23:03, 29 March 2011 (UTC)

The pie chart is nice, and it provides a useful conceptual way to view the energy balance of the Universe, but the numbers are certainly wrong and have been for quite some time now. The numbers in the table further down the page are what should be in the pie chart. Unless someone can make an updated version of it, I recommend removing it from this, and other pages it is linked to. - Parejkoj (talk) 19:05, 4 August 2011 (UTC)

Fate of universe according to ΛCDM[edit]

Wouldn't it be appropriate to include in this article a section on the ultimate fate of the Universe according to the ΛCDM model? I think many people ask for the current best guess for the fate of the Universe. / (talk) 13:19, 8 September 2008 (UTC)

i've added this and sourced a nice cosmology lecture on youtube by lawrence krauss. Macevoy (talk) 18:13, 18 December 2009 (UTC)

Temperature of dark matter[edit]

It would also be surprising if the temperature of dark matter were absolute zero.

What is the reason for expecting a zero temperature ? Dark matter interacts gravitationally (and propably weakly) with normal matter, though the effect is very small, it should be enough to increase the temperature. Also zero (viral) temperature would mean gravitational collapse and surely the Big Bang would requiere higher temperatures. This sentence is irritating and so I propose to delete it —Preceding unsigned comment added by (talk) 17:38, 16 June 2009 (UTC)

History of Lambda-CDM model[edit]

Can someone add some information about the development of this model? Who proposed the use of this model for the first time? When? How has this changed along these years? Was it proposed by NASA? An individual cosmologist? A group of cosmologists?George Rodney Maruri Game (talk) 04:04, 20 January 2011 (UTC)

Schematic diagram[edit]

I've added to the article a schematic diagram of the Lambda Cold-dark matter model. This is an artists interpretation of the standard model of big bang cosmology: Concordance model, ΛCDM or Lambda-CDM. The time-line extends from the big bang/inflation era, 13.7 Gyr ago, to the present cosmological time. This diagram attempts to illustrate the accelerated expansion in two-dimensional spherically symmetric form. Both HUDF and COBE images are used, albeit transformed. It is meant as an aid only in the visualization of such a model. Coldcreation (talk) 04:42, 18 May 2012 (UTC)

Remove assumption of flatness[edit]

That's not part of the model. It's an observation that the universe is close to flat, but the model will handle non-flat universes fine.

  • The model assumes a "flat" spatial geometry, which means that the interior angles of a triangle defined by three beams of light will sum to 180°; space is defined by straight lines. (Alternative geometries include a spherical or "closed universe" in which the interior angles of a triangle would sum to more than 180°, and a hyperbolic or "open universe", in which the angles would sum to less than 180°.) The current values of key parameters imply that the universe is either flat or slightly open, the universe will expand forever, and the expansion is accelerating.

A couple of notes[edit]

A couple of things that could be improved:

  • "It is the simplest model that is in general agreement with observed phenomena; however, a small minority of astrophysicists have challenged the validity of the model." -- plenty of astrophysicists have proposed alternatives to ΛCDM. It's a model that leaves several conspicuously blank spaces, so I think any cosmologist would agree that ΛCDM should eventually be replaced by something more complete. I'm not sure what it would mean to challenge its validity as such, unless we had somehow incorrectly calculated the properties of a ΛCDM universe (so that a ΛCDM universe is not what we think it is).
  • "Historically, the dominant cosmological model previous to the now "standard model" was the Steady State theory, proposed independently in 1948 by H. Bondi & T. Gold and by Fred Hoyle." -- if the standard model means ΛCDM here, then there was a huge gap between steady state and the standard model. I'm also unconvinced that Hoyle, Bondi, and Gold's steady state was ever really the dominant cosmological model. It's true that most astronomers two decades before assumed that the universe was unchanging on the largest scales, but that's quite a different thing from the specific steady-state cosmology that Hoyle and others developed. Their steady state model was from the start an alternative to the Big Bang cosmology.

I would work on fixing these, but I don't have time right now to do it well. Can help look with sources if someone wants to take it on. --Amble (talk) 17:50, 22 June 2012 (UTC)

Definitely agree with the second point. Steady State was the assumption prior to the Hubble et al.'s observations, but it wasn't Hoyle's version. I'm not sure about how to reword the first part; there have been several proposed alternatives, but none of them have gotten significant traction, mostly because LCDM fits the data so well. - Parejkoj (talk) 12:37, 23 June 2012 (UTC)
Quintessence is an example of a very popular alternative to ΛCDM. The term ΛCDM is often used in the sense of "plain-vanilla ΛCDM" without inflation or other features, so I suppose it becomes a matter of terminology whether a particular model is an alternative to ΛCDM or a variety of ΛCDM. --Amble (talk) 15:40, 23 June 2012 (UTC)
I've made a first pass at the intro. Feel free to revert, further edit, etc., with discussion here. This source may be useful: A. V. Filippenko, The Accelerating Universe and Dark Energy: Evidence from Type IA Supernovae. Lect. Notes Phys. 646, 191-221 (2004). [1]. --Amble (talk) 16:47, 29 June 2012 (UTC)

Just my 2 cents, but it a vast relief to see that General Relativity is neither mentioned nor referenced in this. It is not as if GR has been experimentally verified time after time and must be the basis for any cosmological model (at this time). This article seems to suffer a few problems (as I see it) 1. 5% normal matter - isn't it more like 4% (best estimates) ? 2. single originating event - weasel wording for "creation". I categorically denounce any attempt to include the creation event in ΛCDM. ΛCDM becomes relevant immediately AFTER the singularity. We have NO physics nor mathematics that currently deals with singularities in space-time. and 3) The outline is terrible: no quark-gluon plasma? Expansion RESULTS in cooling? Decoupling of the forces? Recombination? Reionization? Structure of the Cosmos? Gravitational effects? and 4) yeah add compliance with GR and possibly different possible meanings of what is meant by "universe" and expanison. (talk) 17:27, 30 June 2012 (UTC)

Article suffers from excessive advocacy bias. Orrerysky (talk) 20:40, 30 November 2013 (UTC)

This is a false claim here. Just because it is a difficult topic does not mean it has this kind of bias. Your "excessive advocacy bias" claim is mostly irrelevant. Arianewiki1 (talk) 09:22, 1 December 2013 (UTC)

Citations Needed[edit]

18:19, 1 December 2013‎ Parejkoj (talk | contribs)‎ . . (21,275 bytes) (-564)‎ . . (Undo POV pushing CN tags by pseudo-science editor.) (undo | thank)

User:Parejkoj undid request for citations. Unsupported statements in the article are not self-evident and require proper citation. Orrerysky (talk) 18:40, 1 December 2013 (UTC)

The revert was to correct disruptive tag bombing and I support it 100%. jps (talk) 22:33, 1 December 2013 (UTC)
I was going to say that we maybe actually did need some citations to that effect, but the first two citations actually are perfect here: Kroupa et al., for the term "concordance cosmology", and Liddle's textbook for why it's the standard model. So, I think we're fine here... - Parejkoj (talk) 00:40, 2 December 2013 (UTC)

Big Bang as "sudden appearance"?[edit]

Hello, I'm normally aroung in the German wikipedia, but I came here for reading something up and I was just puzzled by the following formulation:


I think that this formulation is very bad since it states something of "appearance". How can a space-time appear? One should be very careful with such formulations as one gets the impression that someone could have looked from outside and seen the universe "appear". I'd rather say, "come into existence" or something similar. Do you agree? --Ein Zaungast (talk) 21:58, 10 September 2014 (UTC)

Where's the maths?[edit]

Since the model is supposedly based on general relativity there must be some mathematical background to it which defines and uses the quoted parameters. Where is it? Since the space is assumed flat it presumably uses the Einstein-de Sitter equations. And then there must be a lot of thermodynamic equations as well. At present it's all a mystery.JFB80 (talk) 17:41, 2 December 2014 (UTC)

Are you asking for better coverage of the math in this article, or better references for the details of the mathematics? The second reference in the article is Liddle's cosmology book, which is quite good. That said, it might be good to have a few more textbooks as "Further Readings". - Parejkoj (talk) 19:05, 2 December 2014 (UTC)
Which maths in the article are you talking about? I see only one equation:  p = - \rho c^{2} . Otherwise there is only verbal description and a list of numerical values of parameters. Shouldn't the parameters be associated with their defining equations? A list of parameters is not a model. The book of Liddle is readable but unreliable. For instance he discusses the expansion of the universe by Newtonian dynamics and attributes it to Friedmann whereas this approach is due to Milne (and McCrea). Also he uses classical Maxwell-Boltzmann statistics for the Big Bang - not even using special relativity! JFB80 (talk) 18:32, 3 December 2014 (UTC)
Including some more mathematics in the article is a good idea: why don't you try to add some? However, full derivations of many of the topics of this article require far more length than is appropriate here, so we're better off with good references. As to Liddle's approaches to the topic, they are a great way to explore the behavior of different cosmologies at the advanced undergraduate level; no SR or GR is needed for a lot of this stuff. I suppose we could cite Peebles Principles of Physical Cosmology, though it's not specifically LCDM. - Parejkoj (talk) 20:26, 3 December 2014 (UTC)
Not being a professional cosmologist I was interested to see included the actual relativistic equations used by the professionals, i.e. their model with parameters included. Lengthy full derivations would not be necessary as is normal Wikipedia practice. As regards Liddle I now understand from your comment why he uses these simplifications but even so he should quote the correct origins for the methods used. JFB80 (talk) 20:54, 4 December 2014 (UTC)JFB80 (talk) 07:22, 6 December 2014 (UTC)