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16th November 2022, 08:09 AM  #241 
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This one?
https://arxiv.org/abs/2211.04492 Far from it. But as far as nothing new, I can predict lookback times using a Hubble's constant that is actually constant. 
16th November 2022, 08:35 AM  #242 
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That's an interesting observation.
Comparing the paper to his JavaScript implementation you can see that lookback time somewhat stands alone: Code:
// Lookback time lookback = timeint(1., z1) * Tnorm // Angular distance DA = DL / (z1 * z1) // Lunghezza in primi corrispondente a 1 Mpc. angle = (60. / rad) * z1 * z1 / DL; // Length in Mpc corresponding to 1 degree on the sky R = rad * DL / (z1 * z1); 
16th November 2022, 10:33 AM  #243 
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Nope, you are talking about a way of describing redshift to explain the evidence it provides for accelerated expansion. The ISW and BAO observations have nothing to do with redshift. So, forget the redshift, you need to deal with them as a minimum before even bothering with redshift.

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16th November 2022, 11:00 AM  #244 
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16th November 2022, 09:05 PM  #245 
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One would hope to see a discrepancy, since Ω_{M}=1 is not at all consistent with mainstream cosmology's estimates of that parameter.
Are you telling us that Helland physics expects Ω_{M}=1? Or does Helland physics expect Ω_{M}=0, as you told us you assumed when deriving your Helland equation for a relationship between red shift and distance? 
16th November 2022, 09:38 PM  #246 
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17th November 2022, 10:50 AM  #247 
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Helland's equation is d = (z/(1+z)) c/H_{0} Why don't you quit dancing around and just tell us the values of the parameters that are wired into your Helland equation? You have insisted throughout that your Helland equation is based upon mainstream physics. But the mainstream equations that relate distance to red shift are considerably more complicated than your Helland equation, partly because that relationship is modeldependent. Unlike mainstream equations, your Helland equation mentions no model parameters apart from H_{0}. That means your Helland equation implicitly assumes certain values for the other model parameters on which mainstream equations depend. What parameter values did you assume when you formulated your Helland equation? 
17th November 2022, 11:26 AM  #248 
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17th November 2022, 06:07 PM  #249 
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So you believe
z = d / ((c/H_{0})  d)is a mainstream physics equation? Citation needed! According to your Helland equation d = (z / (1+z)) c/H_{0}a red shift of z=1 corresponds to a distance of about 7 billion light years. According to mainstream physics, a red shift of z=1 corresponds to a proper distance of about 10 billion light years, or 7.7 billion light years if you naively multiply the lookback time by the speed of light. Even with the most charitable interpretation of your Helland equation, it's about 10% off from the best estimates of mainstream physics. 
18th November 2022, 11:17 AM  #250 
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Sorry? The EVIDENCE says the universe is accelerating in its expansion. And those observations do not all include redshift. As mentioned, the ISW and BAO observations strongly support an accelerated expansion. The former, at least, was predicted.
So, faffing around with redshift equations is not going to make those predicted observations disappear, is it? Just as the CMB is not going to disappear, regardless of crank claims about what JWST has shown. 
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18th November 2022, 12:26 PM  #251 
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No. This is a mainstream physics equation 1+z=Eemit/Eobs.
I just inverted it, so the range of redshifts is a percentage, which is what that integral is doing anyways.
Quote:

18th November 2022, 02:13 PM  #252 
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Nope, that is an approximation, and only valid at small z. In other words <<1.
Quote:
What it does not imply is that the universe is not expanding. Use whatever value you can find, and it leads to the same conclusion. People who want static universes need not only to overturn the redshift evidence, they need to overturn, and explain at least as well, the other observations, which show that we are in a universe which is accelerating in its expansion. Nobody can. Which is why nobody is even bothering anymore. 
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18th November 2022, 04:43 PM  #253 
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Nope, that is how redshift z is quantified.
Your thinking of the redshiftdistance relationship. If you try to use with d = cz / H_{0}, you will find this equation to be an approximation. However, by inverting the redshift function, you are multiplying c/H_{0} by a percentage (rather than to infinity). Which is what the lookback integral is doing too. 
18th November 2022, 06:58 PM  #254 
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Prior to 1998, it was thought that Ω_{M}=1.
Since that was younger than the oldest stars, that couldn't be right. Using supernovae data they figured there needs to be the right amount of dark energy to negate the effects of matter. That ends up being Ω_{M}=~0.3 and Ω_{Λ}=~0.7. Redshifts in Helland physics (your name) aren't affected by gravity, so dark energy isn't necessary to counteract its affects. 
18th November 2022, 08:08 PM  #255 
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No. That "1+z=Eemit/Eobs" does not mention d at all, so it cannot be inverted to obtain an equation for d.
The only equation that could possibly be inverted to obtain your Helland equation d = (z/(1+z)) c/H_{0}is z = d / ((c/H_{0})  d)or some algebraic equivalent of that equation. Unsurprisingly, you have been unable to find a citation for any such equation in the mainstream literature. That refutes your claim that your Helland equation was derived by inverting a mainstream equation. It takes a special level of cluelessness to think Ω_{M}=1, taken in isolation, tells you anything about the age of stars. To infer anything about the age of stars, you have to combine that parameter with other observations and with the details of a mathematical model. I'm away from my library at the moment, but when I get back I will give you citations showing that mainstream cosmology of the 1970s was already estimating Ω_{M} to be considerably less than 1. ETA: This spoiler contains the promised citations and quotations, obtained from an online search instead of my library. In mainstream physics, redshifts are affected by gravity, and the mainstream equations for estimating distance from redshift therefore have to take gravity into account. That is yet another proof that your mainstream equation for distance as a function of red shift is incompatible with mainstream physics. 
19th November 2022, 01:59 AM  #256 
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I never said it did.
Quote:
My equation for blueshift is just the equation for redshift inverted. My equation for blueshiftdistance relatoinship is a conjecture. If d = zc/H_{0} was what was initially thought to be redshiftdistance relationship, but we discovered it was inaccurate over most of its domain, then I conjectured d = bc/H_{0}. It's not easy to compare two equations that have different variables, but since 1+b=1/(1+z), then b=1/(1+z)1.
Quote:
"Coupled with the theoretical expectation of Ω m ∼ 1, the low expansion age implied by these measurements, still a few Gyr younger than the oldest stars, set off another “Hubble tension” until the discovery of cosmic acceleration amended the composition and recent expansion history and the age of the Universe grew comfortably higher." 
19th November 2022, 04:11 AM  #257 
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What you did say is that you obtained your Helland equation involving d by inverting that equation, which does not even mention d.
From those facts, it has long been clear that your oftrepeated claim about your Helland equation being consistent with mainstream physics is false. From your ongoing attempts to deflect attention away from those facts and that conclusion (of which your "I never said it did" is just the most recent example), it is fair to conclude that your oftrepeated claim about your Helland equation being consistent with mainstream physics is not just false, but an outright lie. Here is the context, which I quoted just a few posts above: Now you say: In other words, you took an equation that, in mainstream physics, had long been known to be an approximation useful only at small redshifts, messed with it enough to confuse yourself ("It's not easy to compare two equations that have different variables"), obtained your Helland equation by (in effect) multiplying by z (a modification you have yet to explain or justify), and used that Helland equation to calculate distances corresponding to large redshifts that are far outside the domain of applicability of the mainstream equation you are now citing as (apparently) the sole basis for your Helland equation. Which was silly, but here's what was really dishonest: When you believed your silly Helland equation led to inconsistencies, you alleged that was a problem for mainstream physics, rather than a problem for Helland physics. When pressed on that, you say silly things about mainstream physics. This is a recent example: As I wrote earlier, it takes a special level of cluelessness to think Ω_{M}=1, taken in isolation, tells you anything about the age of stars. To infer anything about the age of stars, you have to combine that parameter with other observations and with the details of a mathematical model. Besides, you have the history all wrong. The density parameters are fractions of the critical density. Mainstream theorists wanted the sum of those fractions to add up to 1 (the critical density), because observational evidence was consistent with a flat or nearly flat universe, and a flat universe simplifies the theory. Mainstream theorists also wanted Ω_{Λ}=0, because a zero cosmological constant also simplifies the theory; besides, Einstein regretted his addition of that constant to his field equations (even though, mathematically speaking, that constant belonged in his field equations just as much as the constant that belongs in a calculus student's solution for an indefinite integral), and Einstein's opinions were pretty influential. A problem arose when, beginning in 1976 and further confirmed in 1983, calculations based on actual observations strongly suggested Ω_{M} ~ 0.3. The theorists didn't like that, as was mentioned in my quotation of a 1995 paper. By 1998 or thereabouts, the discrepancy between Ω_{M} ~ 0.3 and the theorists' desires was resolved when the theorists gave up on their idea that Ω_{Λ}=0. That is what Reiss was talking about: I have highlighted some phrases you misunderstood. Ω_{M} ~ 1 was a "theoretical expectation" on the part of theorists who wanted the simpler theory you get with flat spacetime and a zero cosmological constant. Unfortunately for the theorists, the best estimate based on mainstream physics was Ω_{M} ~ 0.3. That estimate has been pretty stable since the mid1980s, when it improved upon the 1976 conclusion that Ω_{M} < 0.5. If you combine Ω_{M} ~ 0.3 (based on measurements) with Ω_{Λ}=0 (which was based upon little more than the theorists' hopes and Einstein's influence) and plug those values (along with some others) into the FLRW models for an expanding universe, you get an age for the universe that is younger than the apparent age of some extremely distant objects. That is the "Hubble tension" of which Reiss spoke in your quotation. Reiss's "amended...composition" of the universe was achieved by retaining the Ω_{M} ~ 0.3 estimate of the 1980s while accepting the reality of dark energy in the form of a nonzero cosmological constant, with Ω_{Λ} > 0. 
19th November 2022, 04:34 AM  #258 
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False.
You keep saying "Helland equation" but you keep confusing two different things. 1 + z = E_{emit} / E_{obs} That's a mainstream equation for redshift. Invert it. What do you have? 1/(1 + z) = E_{obs} / E_{emit} You can call that the Helland blueshift equation if you'd like. 1+b =1/(1+z) That's how the two values are related. Now I find this interesting, because while the range of z for valid redshifts is 0<z<infinity, the range of b for valid redshifts is 1<b<0. z goes to infinity, while b only goes to 1. Let's look at the lookback time integral. t(z)=1/H_{0} * an integral As z goes to infinity, t approaches 1/H_{0}. It will never get larger than that. So the integral must go from 0 to a limit of 1 (rather than infinity). I could just do this t(z)=1/H_{0} * b. You can call that the blueshiftlookback time relationship if you want. I can also propose d = bc / H_{0}, since d=ct. You can call that the Helland blueshiftdistance relationship if you want. But you're just being confusing by giving different things the same name. 
19th November 2022, 05:13 AM  #259 
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That's Cappi's equation (7).
Yes, someone who is truly ignorant of calculus might do that, thinking your Helland equation for t(z) is consistent with Cappi's equation (7). But your Helland equation for t(z) isn't consistent with Cappi's equation (7). Guessing that the integral is always equal to b is not at all the same as computing the value of the integral. By the way, the value of the integral in Cappi's equation (7) depends upon several model parameters, including Ω_{M}, Ω_{R}, and Ω_{Λ}. Your Helland equation for t(z) doesn't mention any of those parameters, so it is freaking obvious that your Helland equation for t(z) is not consistent with Cappi's equation (7). If you want, you can call it the Helland equation for the blueshiftlookback time relationship. But you cannot truthfully say your Helland equation for whatever you want to call it is consistent with mainstream equations such as Cappi's equation (7). You are the ultimate authority on Helland physics, so you can propose whatever idiocies you like. But you cannot truthfully say your proposed idiocies are consistent with mainstream physics. 
Last edited by W.D.Clinger; 19th November 2022 at 05:23 AM. Reason: corrected tags so Cappi's equation will be displayed 

19th November 2022, 05:25 AM  #260 
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You've dubbed one of my equations as the Helland equation.
And then another one of my equations as the Helland equation. And then you talk about them interchangeably. I only derived 1/(1+z)=E_{obs} / E_{emit}. I derived the blueshift equation by inverting a mainstream redshift equation. Those equations are not distance or time relationships. Those I invented. I modified the broke d=cz/H_{0} by replacing z with b: d=bc/H_{0}. That wasn't derived. That was just conjectured. So the different equations came about in different ways.
Quote:
Quote:
I didn't say all my equations are consistent with mainstream physics. 
19th November 2022, 05:46 AM  #261 
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Thank you. So far as I know, this is the first time you have actually admitted that your d=(z/(1+z))(c/H_{0})equation was your own invention/conjecture. The d=(z/(1+z))(c/H_{0}) equation you invented/conjectured was the equation you were using to calculate the distances that, according to you, were a problem for mainstream physics. If there was a problem with the distances you calculated using an equation you invented/conjectured, that is a problem with Helland physics, not a problem for mainstream physics. To suggest that the failures of Helland physics are a problem for mainstream physics is dishonest. 
19th November 2022, 05:53 AM  #262 
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I said it straight away.
http://www.internationalskeptics.com...&postcount=126
Quote:

19th November 2022, 06:19 AM  #263 
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19th November 2022, 06:52 AM  #264 
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19th November 2022, 07:13 AM  #265 
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https://en.wikipedia.org/wiki/Redshift
If the photon is emitted with 1 eV, and observed with 0.5 eV, 1/0.51=1. You would only get negative numbers of emit < observe, but that's blueshift.
Quote:
b = Eobs/Eemit 1 If the photon is emitted with 1 eV, and observed with 0.5 eV, 0.5/11=0.5. So z=1 is equal to b=0.5. 1+b=1/(1+z) A CMB photon has a z=1100 and b=1100/1101=0.999091. CMB lookback time is b/H_{0}. 
19th November 2022, 08:04 AM  #266 
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And then, three days later, you claimed that equation calculates results that are "exactly equal to LCDM in a default state": I did not begin to dispute your equation giving d as a function of z until you had claimed your equation was "exactly equal to LCDM in a default state. Here is the first exchange in which I began to discuss your equation: And then you began to say your calculations showed that an "expanding universe is internally inconsistent": You cannot perform standard redshift or lookback calculations using the equation d = (z/(1+z))(c/H_{0})As you acknowledged an hour or so ago, you invented/conjectured that equation. ETA: Several posts back, I was trying to get you to tell us the model parameters assumed by your equation above, but you danced and squirmed instead of answering the question. It turns out that if you assume Ω_{M} = Ω_{R} = Ω_{Λ} = 0, then Cappi's equation (7) reduces to t(z) = (1/H_{0}) (z/(1+z)). It seems therefore that your Helland equation for computing d from z assumes a universe devoid of matter, devoid of radiation, and devoid of dark energy. Do you think that explains why your invented/conjectured equation yields calculations that differ from calculations based on mainstream physics, with mainstream estimates of those parameters? 
19th November 2022, 08:45 AM  #267 
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Right.
Default as in before you add stuff to it, like matter, dark matter, and dark energy, and give it curvature.
Quote:
Originally Posted by Mike Helland
Quote:
Repulsive dark energy cancels out the effects of attractive matter (including dark matter), but kinda sloppily. I made this tool to show it, using Cappi's code. Start empty, then add matter, 0.3, then dark energy. Or just read post 234 It seems to me that as distance measurements get better, any discrepancy can be tested by observation. *edit* forgot link: https://mikehelland.github.io/hubble...other/lcdm.htm 
19th November 2022, 09:27 AM  #268 
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But I'm not sure that's right, because...
I logged back in to correct this:
Quote:
t(z) = (1/(2H_{0})) (z/(1+z))when you assume Ω_{M} = Ω_{R} = Ω_{Λ} = 0. Well, it's possible I'm mistaken about the factor of 1/2. I didn't intend to ask a trick question, it just turned out that way. I'll check my calculation later when I have more time. The integral is greatly simplified by assuming Ω_{M} = Ω_{R} = Ω_{Λ} = 0, but I might have made a mistake while tracing the E(z) of equation (7) back through its defining equation (4) and the definitions preceding equation (4). In particular, I need to check whether the other density parameters really imply Ω_{k}=1 using Cappi's definitions. As you can imagine, I haven't spent a whole lot of time contemplating the quantitative relationship between redshift and distance in a completely empty universe that, even so, has enough curvature to achieve the critical density. And by the way, I suspect the calculators you've been using will automatically calculate that curvature parameter from the values you specify for Ω_{M}, Ω_{R}, Ω_{Λ}, and H_{0}. I'm doing this by hand. 
19th November 2022, 09:37 AM  #269 
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The calculator code I'm using is Cappi's, referenced in the first paragraph:
"This short introduction is extracted from a paper on cosmological models with a dark energy component (Cappi 2001). For an on–line implementation of cosmological formulae see www.bo.astro.it/∼cappi/cosmotools." Code:
Omega_k = 1.  Omega_M  Omega_L; 
21st November 2022, 07:41 AM  #270 
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21st November 2022, 09:16 PM  #271 
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k < 0 indicates negative curvature, and Ω_{k}=1 indicates a great deal of curvature. As for the numerical value of k, there are two different conventions.
I haven't looked at that specific calculator, but k is often taken to be a discrete parameter constrained to have one of these three values:
I normally use the other common convention, in which a(t) is a dimensionless scale factor expressed as a fraction of the presentday scale, and k is the Gaussian radius of spatial curvature at the present day. The fact that Cappi's convention is different from the one I tend to use might cause confusion if you're trying to compare my notes on the Friedmann equations for flat space with Cappi's. ^{*}In many of my recent posts, I have written "flat spacetime" when I meant "flat space". Sorry about that. 
21st November 2022, 09:51 PM  #272 
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22nd November 2022, 06:28 AM  #273 
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The second part is true as well.
Ω_{k} is the curvature parameter, defined as the fraction of the critical density by which the sum of the matter, radiation, and dark energy parameters falls short of the critical density. When those other density parameters add up to 1, Ω_{k}=0 and there is no curvature. When all of those other critical densities are 0, Ω_{k}=1, implying a great deal of curvature. Taking H_{0}=70 km/s/Mpc, Ω_{k}=1 implies the radius of curvature is approximately 140 billion light years. With k=1, that's a negative curvature, meaning space does not close upon itself, but opens upon itself. Ω_{k}=1 is hundreds of times more curvature than would be consistent with the Planck mission's observations:
Originally Posted by Wikipedia

22nd November 2022, 07:10 AM  #274 
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Right, so when Ω_{K}=1, then it falls short of the critical density by 100%.
You said:
Quote:
Quote:
"It is customary to express the density as a fraction of the density required for the critical condition with the parameter Ω = ρ/ρ_{critical} so that Ω = 1 represents the condition of critical density. " p = 0, so Ω = 0, and Ω_{K} = 1. 
22nd November 2022, 09:09 AM  #275 
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Right, assuming the antecedent of the highlighted pronoun is the sum of the matter, radiation, and dark energy parameters.
Right, assuming the highlighted pronoun refers to the sum of the matter, radiation, and dark energy parameters. My highlighted phrase was a poor joke, intended to highlight your mistake in this post:
Originally Posted by Mike Helland
The highlighted phrase told me that, when you wrote that, you thought the calculator you were using defaulted to parameters corresponding to a completely empty universe, devoid of matter and devoid of energy, with no curvature. You were unaware that your calculator automatically supplied enough curvature to make up for the failure of the ordinary density parameters to add up to the critical density. 
22nd November 2022, 09:14 AM  #276 
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22nd November 2022, 09:28 AM  #277 
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You didn't really have to convince us you don't understand the concept of curvature in geometry, but I agree about your remarks being good for a laugh.
Originally Posted by Wikipedia
ETA: Here's a picture. 
22nd November 2022, 12:11 PM  #278 
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So, an empty FLRW universe only expands, and has an open geometry.
Fill it up with just the right amount of matter (and/or radiation) the expansion and gravity will be in balance, with is flat. And if it has more matter than that, gravity will overpower expansion and it is closed. But you could add repulsive dark energy to push it back to flat or open. So did you figure out how that lookback integral reduces? H_{0} or 2H_{0}. 
22nd November 2022, 01:22 PM  #279 
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Not exactly. You apparently do not understand that the FLRW models are an entire family of mathematical models.
One of the FLRW models is for an empty universe with flat space (zero curvature). That's because the general theory of relativity reduces to special relativity. Because you were playing around with a calculator whose models and parameters you did not understand, you told it to assume a completely empty universe with a positive Hubble constant. (I don't know whether you specified the Hubble constant yourself or let the calculator choose a default positive value for the Hubble constant, but I also don't much care how you screwed up.) With those assumptions, special relativity doesn't apply because of the positive Hubble constant. To accommodate the Hubble constant you specified (whether explicitly or implicitly), the calculator had to assume a lot of negative curvature to account for how you could have that Hubble constant despite empty space. If the matter, radiation, and dark energy densities add up to the critical density, then space will be flat. Note, however, that flat space is entirely consistent with expansion, even with an accelerating expansion, and that is the conclusion to which we are led by observations that imply realistic values for the density parameters. ETA: By the way, the distinction between flat and curved is not the same as the distinction between open and closed. Well, if it has more matter etc than the critical density, then spacetime is closed in the sense that gravity will eventually overpower expansion, leading to a Big Crunch. But even that conclusion is based upon the FLRW models, and mainstream cosmologists are willing to consider effects that are not considered by the FLRW models. Which is, at the moment, the mainstream explanation for why the universe is flat to within measurement error... ...instead of being hundreds of times more curved than would be consistent with measurements, which is the scenario you hilariously described as "LCDM in a default state". It took me a while to understand what you were smoking when you wrote that. By the way, I am not suggesting you were being ridiculous on purpose. Within the next couple of days, I hope to finish my calculations and write them up for public consumption at this forum. Inspired by your "LCDM in a default state", I will do the math for your "LCDM in a default state" as well as for a variety of other simple models that are just as far out of touch with reality, mainly because I know how to compute closed form solutions for the integrals that come up when calculating with those simple models. Then I will use numerical integration to do the math for a couple of more realistic models. I prefer to present all of those calculations within a single long post. 
22nd November 2022, 01:43 PM  #280 
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I look forward to it.
The first parameters I compared to my distance relationship were Ω_{M}=0.3 and Ω_{Λ}=0.7. The blue line shows the difference between them. Considering I just went "what about quantifying redshift as negative blueshift" and use that in the distance relationship, I was pretty shocked it was actually that close. So you can imagine that finding they match exactly when you remove the effects of gravity and dark energy was completely not what I was expecting to find. 
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