Talk:Friedmann equations

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Friedmanns original equation could not possibly have included the term "a(t)"!

... because a(t) wasn't invented until four years (1929) after his death (1925)!

A presentation of the original equation would be quite interesting. Hilmer B (talk) 15:18, 19 August 2020 (UTC)[reply]

Do you have any reliable source to back up that statement? JRSpriggs (talk) 19:34, 19 August 2020 (UTC)[reply]

Do you have any reliable source to falsify that statement? Did really Friedmann invent and use "a(t)" as it is interpreted today? Hilmer B (talk) 19:46, 20 August 2020 (UTC)[reply]

To a mathematician using the radius of a hyper-sphere as a function of time when the hyper-sphere varies in size is obvious. If you need to see that Friedmann was aware of it, see his letter to Ehrenfest here where he says "a world, the space of which possesses a curvature radius varying with time;". JRSpriggs (talk) 20:44, 23 August 2020 (UTC)[reply]

I guess you're referring to II:1 in that letter: “From my second note in Russian that I have sent to you, you have seen that under certain assumptions common to those of Einstein and De Sitter it is possible to obtain the universe with the space of a (spatially!) constant curvature, the radius of curvature of which is varying with time.”

Friedmann does here not suggest that he shared the belief that the scale of space itself varies with time, or ?! It may rather suggest that he, himself, considered spatial variations in the curvature. No trace of an expanding “a(t)” universe i this statement.

The quality and the beauty of Friedmann's equation is rather the way he relates the curvature of spacetime to (the local) density. He may very well have allowed the curvature to vary in space. What Einstein-deSitter suggested was a variation also in the time dimension. My guess is that they were worried because their interpretation of ∇2Φ = 4πGρ did only allow positive curvature in a static universe . (∇2Φ > 0 ...)

So back again to the original question: I guess that we can both agree upon that 1/R2 should have appeared in Friedmann's original, and I guess only, version of this equation. But was it also 1/a2(t)R2? And in that case how was that a(t) defined? Exactly: what did Friedmann's original equation look like? Hilmer B (talk) 19:07, 24 August 2020 (UTC)[reply]

Unfortunately, the original papers of Friedmann are behind a wall: you have to pay to see them and then they are in Russian or German. This is a common problem, forcing us to rely on secondary sources. But the mere fact that those papers are not available to us is not evidence that Friedmann was unaware of what is now purported to be their contents. JRSpriggs (talk) 19:30, 24 August 2020 (UTC)[reply]

Weird - Friedman died 95 years ago. Not even Disney has managed to get such a prolonged protection ... So - the conclusion is that none of us knows. A case similar to the situation of Schrödinger's poor cat ... Well, thanks for your contribution. Hilmer B (talk) 20:39, 25 August 2020 (UTC)[reply]

Justification for eliminating the Cosmological Constant from the First Equation

You properly derive the first equation as:

${\frac {{\dot {a}}^{2}+kc^{2}}{a^{2}}}={\frac {8\pi G\rho +\Lambda c^{2}}{3}}$

But then you go on to state that:

These equations are sometimes simplified by replacing

$\rho \rightarrow \rho -{\frac {\Lambda c^{2}}{8\pi G}}$

to give:

$\left({\frac {\dot {a}}{a}}\right)^{2}={\frac {8\pi G}{3}}\rho -{\frac {kc^{2}}{a^{2}}}$

What is the justification for this substitution? I might guess that you assume that the Cosmological Constant is so small with respect to the other terms that it is effectively zero, but you can't just drop a major variable without an explanation.

It is a question of how the cosmological term is interpreted. Is it a complication in the law of gravity (as originally conceived)? Or is it a mysterious "dark energy" which should be included in the stress-energy tensor on the other side of the equation? Lately, people have been leaning to the latter interpretation. JRSpriggs (talk) 03:31, 21 February 2021 (UTC)[reply]

The Friedman's equations and the problem of entropy

The Friedman's equations don't have equations with entropy and this problem is weird 164.127.230.76 (talk) 12:32, 11 September 2024 (UTC)[reply]

Inappropriate value of Hubble constant.

@MasihZarafshan added a computation in this edit which I believe is not appropriate.

First of all it uses one value of the Hubble constant when in fact today there are famously two different values. Using only one is a point of view. (Also in my opinion if you must pick on Hubble value in the founding equation for Big Bang cosmology you better use the Hubble constant derived from it).

Second the calculation is not sourced and in fact reliable sources do not appear to make this calculation. Reviews and textbooks leave density in a parametric form. If they did an explicit calculation we could just refer to that source.

So: Why is this calculation added? What source tells us this is useful? If we have an answer then we can work on the point of view. Johnjbarton (talk) 03:11, 14 February 2025 (UTC)[reply]

The value H0 = 76.5 ± 2.2 km s−1 Mpc−1 is concluded from "the most precise measurement" of the distance to the Coma cluster published on this article The Astrophysical Journal Letters at January 2025, utilizing the Fundamental Plane relation.

As for you opinion, I have nothing against it, neither does this article as it uses the FP for it's derivations.

I did the calculations which are simply evaluated by compensating the aforementioned H_0. I also made sure to substitute the values as far as the article did before my edit and never beyond, as a sign of respect for previous authors and also not to create loose ends for other pages which might have used that article as a reference.

To conclude, I merely rationalized the equations to match the most up to date measurements. MasihZarafshan (talk) 11:54, 14 February 2025 (UTC)[reply]

Wikipedia's policy is to prefer secondary sources. One important reason is that a primary source like the one you cite will naturally chose to highlight their work. The measurement reported in that source may be "the most precise" but what they don't tell you is that other sources get different answers. Precision is only a characteristic of a statistical measurement, it does not tell you if the measurement is based on incorrect assumptions. Furthermore, such measurements have a long history of revision after publication, so again primary sources that have not been cited are not the best choice.

In the case of the Hubble tension, the cause of the difference between different techniques is not known, but certainly one of the common suggestions involves the Friedmann equations not be completely correct.

The 2024 edition of the Particle Data Group review for Cosmological parameters discusses the measurements of H_0. They give the Lambda-CDM based value of H0 = 68.0+0.4−0.3 km s−1 Mpc−1 and the SH0ES team value of H0 = (73.0 ± 1.0) km s−1 Mpc−1. These are the two values we should use in the article. Johnjbarton (talk) 17:42, 14 February 2025 (UTC)[reply]