Talk:Redshift

Redshift of gravitational waves

The lead says, "Gravitational waves, which also travel at the speed of light, are subject to the same redshift phenomena." But then it would be true that gravitational waves are subject to redshifting by gravitational potentials. Is this true? Praemonitus (talk) 18:07, 28 October 2023 (UTC)

Charts and age/lookback calculation

Hi @Parejkoj: regarding [1], could you please give me more actionable criticism than "not sure these are a good fit"? I worked hard to make charts the lay readership can actually use when interpreting the groundswell of very early JWST observations filling the news these days. The existing proper distance plot you favor goes to z=10,000 so fully half of it will almost certainly never correspond to any observations, and the log scale axes aren't at all layperson friendly. My charts are designed to do what laypeople readers are most likely going to want to do when they read a z number, and do it clearly and easily. I am most interested in learning how you think they may be improved.

As for the equations, there are already no fewer than thirty-six display equations in this article, including lengthy integral solution derivations which have nothing practical to do with redshifts. Let me ask you, if someone gives you a redshift value, and asks you to calculate something with it, the age of the universe or lookback time is likely to be pretty high up on the list of possibilities, right? None of the 36 display equations already in this article allow you to calculate those; mine do.

Can we agree to delete the AP calculus derivations instead of the math which is immediately useful for values of the subject of the article? Sandizer (talk) 02:24, 16 November 2023 (UTC)

Seconded. I too would like to understand why this revision makes sense. Praemonitus (talk) 15:56, 16 November 2023 (UTC)

I agree that the big derivation is unnecessary, and I have removed it. I'm not sure the resulting text is fully coherent; please help clean it up! In particular, we could use some links to articles that do said derivation; I don't have access to the textbooks linked at the end of the Expansion of Space section. There are probably other equations in this article that should be removed, as the article itself is quite bloated. That said, I'm not sure how those derivations are "AP calculus" while your integral is not.

If someone gives me a redshift value and asks me to calculate something from it, I'm going to use one of the various numerical integration tools provided by e.g. Ned Wright or astropy.cosmology to perform the calculation (unless I'm a student in a class being asked to write my own numerical integrator). All of the things one would want to calculate are derived from the integral for the FLRW scale factor; I'm not finding that integral written out on any of the obvious pages, so that might be a worthy addition, probably to Scale_factor_(cosmology) or Lambda-CDM_model). The version you added to Chronology of the universe is specific to the current best LCDM parameters, so is not general enough (and probably should be removed from that page, too).

I hadn't noticed that the existing proper distance vs. redshift plot went to z=10,000 (I had noticed that it has far too small of fonts). For its purpose--showing the scale of the universe to past the CMB--that's probably fine. I think two plots like that--one to large redshift, the other to z~15, both showing distance on one axis and lookback time on the other--would be useful, shown side by side. I'd remove the callout to a JWST galaxy: that's going to become outdated very quickly. I'd also remove the values written along the curve: they make it cluttered. I'll try to quickly put together something with astropy and matplotlib. - Parejkoj (talk) 18:56, 16 November 2023 (UTC)

@Parejkoj Thanks! There's source code on the chart file description on Commons. I used Wright's python code to set Omega_Lambda from Omega_mass for a flat cosmology. I really like the numbers along the curve for the more bendy graph, but as that is so uncommon these days I suspect there's a better way. I put in the furthest observation for the labeled current year to give laypeople readers an idea of how far we've come along the range JWST was designed for. Anyway, I can't wait to see what you come up with! Sandizer (talk) 19:07, 16 November 2023 (UTC)

As I said, unless you're in a class, it's almost never worthwhile to code up your own cosmology integrator. Just use astropy.cosmology, which has various cosmologies built-in (or you can set your own parameters directly). Here's my version, with both distance and time. - Parejkoj (talk) 20:04, 16 November 2023 (UTC)

Your graph is far better than the old one, but it is in no way near what layperson and pre-tertiary students might be expected to be able to use when interpreting redshift discussions in the news or their schoolwork, respectively. I replaced the old graph with yours, replaced my two graphs, and replaced the equations showing how to calculate age of the universe and lookback time directly as more immediately practical and useful than the vast majority of the remaining display equations. Sandizer (talk) 12:29, 20 November 2023 (UTC)

Most readers wouldn't be able to use your equations either: they'll need a computer to evaluate the gamma function, at which point they might as well do it properly with one of the available numeric integrators or, even better, one of the many online tools that do it for you. I've removed your expression from the Age of the Universe page as well. We should do a better job linking to the full expressions on Distance measure and Friedmann_equations#Detailed_derivation, but partial solutions to those for a particular choice of parameters don't really belong here.

I'm also skeptical that any lay reader would be able to interpret any of the redshift vs. X graphs we show, and certainly using a graph to get the value of something is not at all a common skill. Graphs are useful for showing the qualitative shape of things, not typically for quantitative analysis (especially when there are equations one can evaluate directly).

With your changes, we now have two graphs of lookback time covering roughly the same redshift range, which seems excessive. Yours I find to be very cluttered, due to all the numbers. Do you really expect readers to read numbers off a wikipedia graph to determine numerical values? Given the section you placed it in, I'd rather remake my plot to go out to at least the CMB (~1000), but then the lookback time isn't very informative (which is why it was a log plot before). I'm also not sure that there's much benefit of having separate lookback time and age plots, and if we do want them, they should probably be just made on the same graph. - Parejkoj (talk) 00:11, 21 November 2023 (UTC)

@Parejkoj: Suppose you read (the hilariously titled for popular treatment) [2], but not the title of the original paper, and you want to know the z values for the "teenage" (2 to 3 billion years after the big bang) galaxies. Which of the two lookback time graphs can you actually do what with? The reason the numbers look like clutter to you is because as a professional you have both the familiarity with tools and skill such that you don't need to depend on actually usable graphs to get answers to common questions. In any case, I'll try putting python alongside the age formulas and see if you like that. It is not an "approximate expression," it's the exact closed form of the integral in parameterized Lambda CDM cosmology, contrary to your edit summary.

To derive the age of the universe from redshift, numeric integration or its closed-form solution involving the special Gaussian hypergeometric function ₂F₁ may be used. For early objects, this relationship is calculated using the cosmological parameters for mass Ω_m and dark energy Ω_Λ, in addition to redshift and the Hubble parameter H₀.

${\text{ageAtRedshift}}(z)=\int _{z}^{\infty }{\frac {1}{(1+z')\cdot {\sqrt {\Omega _{\Lambda }+\Omega _{m}\cdot (1+z')^{3}}}}}\,dz'\cdot {\frac {977.8}{H_{0}}}$

$={}_{2}F_{1}\left({\frac {1}{2}},{\frac {1}{2}};{\frac {3}{2}};-{\frac {\Omega _{\Lambda }}{\Omega _{m}\cdot (1+z)^{3}}}\right)\cdot {\frac {2\cdot 977.8}{3\cdot {\sqrt {\Omega _{m}}}\cdot (1+z)^{3/2}\cdot H_{0}}}\,{\text{Gyr}}.$

Or in Python,

from scipy.special import hyp2f1  # hypergeometric function 2F1 is in integral solution

H0 = 69.32  # Hubble parameter, median of disparate approxiamations
Om = 0.317  # Density parameter for matter Omega_mass from arxiv:1406.1718.pdf p. 8
OL = 1.0 - Om - 0.4165/(H0**2)  # set parameter for dark energy density Omega_Lambda
    # to a flat curvature, from https://www.astro.ucla.edu/~wright/CC.python
    # (on https://www.astro.ucla.edu/~wright/CosmoCalc.html which see)

# Age of universe at redshift z as a closed-form solution to its integral definition,
def age_at_z(z):  # ...which is 27 times faster than the original numeric integration
    hypergeom = hyp2f1(0.5, 0.5, 1.5, -OL / (Om * (z + 1)**3))
    return (2/3) * hypergeom / (Om**0.5 * (z + 1)**1.5) * (977.8 / H0)  # 977.8 for Gyr

Lookback time is the age of the observation subtracted from the present age of the universe:

${\text{lookBackTime}}(z)={\text{ageAtRedshift}}(0)-{\text{ageAtRedshift}}(z)$

Better? Sandizer (talk) 18:59, 21 November 2023 (UTC)

No, there's no point to any of that. As I keep saying, if someone wants to know the age, comoving distance, or lookback time of a given redshift, they'd just use one of the many calculators we link to. Your python above is completely unnecessary, and doesn't allow for changing the cosmological parameters. Why would someone ever use that expression, when they could just call astropy.cosmology for whatever parameters they wanted?

If I wanted to know the lookback time for a JWST galaxy at a given redshift, I'd go to Ned Wright's calculator and just get the exact answer. A lay reader would be much better served by us providing more obvious links to such calculators, than providing ad hoc expressions that factor out multiple parameters. - Parejkoj (talk) 04:39, 23 November 2023 (UTC)

simultaneous

is not the right word for two descriptions of the same thing changing correspondingly. 184.97.176.97 (talk) 03:06, 12 December 2023 (UTC)

Agreed. I removed it as unnecessary. Praemonitus (talk) 04:51, 12 December 2023 (UTC)