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Look 88 billion years into future with the A20 tabular calculator 
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#19
Jan2113, 04:26 PM

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If I understand what I am looking at in the chart, 41/42 mly is way,way off to the right, via the purple curve, 'distance then'.. As I recall that is about 380,000 years after the big bang and a redshift of about 1090. [The chart uses S =1+z, and only goes to S =10, redshift of z = 9. ] In fact I started to try to calculate the distance at z =10, and never found a simple formula....I suspect that's why we have the calculator.... 


#20
Jan2113, 06:30 PM

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As you know, and most other readers as well, YOU decide the range that the table covers. for example if you want it to cover all of history since the CMB flash (which gets stretch 1090) and if you want the table to have 10 downsteps from there to the present (i.e. 11 rows) then you put in: upper=1090 lower=1 step= 10 You can also make it show more, or fewer, decimal places in the answers. So it can give more precision in some columns and round off in other columns. You just type the number of decimal places you want the answer to have, in that column, in the box at the head of the column. 


#21
Jan2113, 07:28 PM

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Here's a result I just now got, to demo the feature where you control the precision. I set it to show 1 decimal place for the Stretch, 4 for the scalefactor a, 6 for the Year, 4 for the Hubbletime, 1 for Dnow, 4 for Dthen, and 3 decimal places for Dhor the event horizon distance:
just set upper=1090, lower=1, step=10 1090 being the stretch factor for the CMB flash and 1 being the stretch factor for the present (i.e. no change in distances or wavelengths, the identity) 


#22
Jan2113, 09:56 PM

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Actually in my calculator I immediately convert the Ys to Omegas, so apart from the user interface and "frontend", nothing else need to change. I will look into the possibility of a Bmodel, returning it to the legacy input parameters, giving people a choice. What do you think? 


#23
Jan2113, 10:11 PM

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(Now CosmoLean_A27, no longer A22). 


#24
Jan2213, 10:19 AM

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Some different scaling for the scale factor entries would be interesting  maybe equidistant logarithm or equidistant scale factor (+optional?). If you want to look at the range of 1090 to 1, for example, you just have a single entry in the stelliferous era, unless you want 100+ lines as output. Entries like (1090, 545, ..., 2, 1) + rounding errors would be more relevant I think.



#25
Jan2213, 10:15 PM

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What do you think of working with Hubble time inputs vs. standards density parameters and Hubble constant as input? 


#26
Jan2313, 09:25 AM

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I think if you want to change those parameters, you usually know how to do that. Density parameters are probably easier to manipulate, however.



#27
Jan2713, 04:19 AM

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After a bit of forum testing and perhaps tuning, we can make it more visible again. 


#28
Jan2713, 09:50 AM

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Jorrie...this model: cool. Thanks for your efforts.!!



#29
Jan2713, 10:05 AM

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Very nice, thanks.
Yinf standard is 16.3, but the tooltip gives 16.9 as best fit? 


#30
Jan2713, 10:32 AM

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Indeed it is very nice! Here's something I just tried with the nonlinear step box checked.
I wanted 20 steps down from 1090 to 1 (from recombination to present) so I put this into google calculator: "1090^.05" and got 1.41863714 That is the 20th root of 1090. So I put in S upper = 1090 S lower = anything less than 1 would do, I happened to put 0.15 step = 1.41863714 (just pasted in from the calculator)



#32
Jan2713, 01:59 PM

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Edit: Done. Also fixed the tooltip mistake. If your cache prevents modified version from loading, try TabCosmoC2.html. It is the same as C1. 


#33
Jan3113, 09:27 PM

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One of the luxuries associated with using the new online Cosmic Tabulator is you can (in seconds) get a whole history of the universe from recombination (the origin of the Background) down to today and on far into the future.
I just tried this to see how it would look if I set it to use 30 steps to get from recombination to Now, and then let it do a dozen or so steps beyond that into the future. What I like about this (besides that it is very quick to get once you decide you want to start at S=1090 and get to the present in 30 steps) is that you see in context a lot of the numbers that we are always hearing aboutthat keep coming up in Cosmo Forum threads. For instance right in the first row you see that the CMB was emitted in year 380,000, by matter that was then 42 million LY away, and is now 45.89 billion LY from us. And you see, from the bottom row, that both the distance to the cosmic event horizon AND the Hubble distance are converging together to 16.3 billion LY. In fact that's what they'll essentially be by year 62 billion. And the Hubble times give you a convenient handle on the expansion rates now, and in the past, and in the future. You can see the present Hubble time (in the S=1 row) is 13.9 billion yearsthis means distances are increasing by 1/139 of a percent every million years. Far in the future, when the Hubble time is stabilizing at 16.3 billion years, distances will of course be increasing by 1/163 of a percent every million years. Then again, if you check out the row around S=2.5 you'll see that, back around year 4 billion, expansion was considerably fasteraround 1/60 of a percent per million years. And the nice thing is you get to see how all these numbers gradually change over time.
And how far will they be from us when the message actually "catches up" to them and gets there? The table says they will be 20.7 times farther than they are today, and that means they will be at a distance of 307.87 billion LY. I keep the link to the calculator in my signature to have it handy. But here it is, a little more visibly: http://www.einsteinstheoryofrelat...abCosmoC1.html As always, thanks Jorrie. It's neat. 


#34
Feb113, 07:02 PM

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I mentioned that if you look down to the last row of the table, around year 60 billion when distances are 20 times what they are at present you will see the important distance 16.3 billion LY.
Both the Hubble distance and the Cosmic Event Horizon distance are converging to that important 16.3you can see that in the table very clearly. That 16.3 billion LY distance is a physical substantive visible form of the cosmological constant Λ. Just take the reciprocal of that distance, and square it, and you have Λ. There is nothing "dark" or mysterious about it. It was a mistake, I think, to ever refer to it as "dark energy". Technically it is a small intrinsic curvature which naturally appears in the Einstein GR equation and whose value was not known until recently (the 1990s). The value might have turned out to be exactly zero, but there was no reason it had to be zero, and as it turned out, it wasn't. 


#35
Feb213, 08:30 AM

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What is this some sort of physicsforums 'quiz'...??
when I look at the bottom row of the table to follow your explanations I see these numbers.... I don't see all the numbers quoted in your text: S a T T _Hub D_now D_then D_hor 1.594 0.627 8.05254 10.269 7.165 4.495 14.305 Am I getting THAT old?? edit: darn!! I just realized there is a scroll bar along the right hand side of the table.... problem solved!! 


#36
Feb213, 02:56 PM

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Naty, I'm glad you saw the scroll bar and worked that out.
Just in case you are curious. the 73% we are always seeing is not a CONSTANT. It is a temporary figure that gives a handle on Lambda that depends on present conditions. Here is how to get it from the Hubble times 13.9 and 16.3 billion years. Just calculate the ratio of their squares: 13.9^{2}/16.3^{2} = .73 13.9 billion years is information about the present, it is 1/H_{o} the reciprocal of the current fractional rate of distance expansion. 16.3 billion years is the corresponding thing way out in the future. THAT is the cosmological constant, in essence. =========================== People who talk about Lambda as if it were a curvature that arises from a certain dark "energy" do not normally tell you what actual energy DENSITY it corresponds to in real terms like nanojoules per cubic meter. Normally they only tell you the temporarily valid handle 73%. But I'll tell you how to get your hands on that energy density, in metric, just from the 16.3 figure. [Footnote: If you know metric units you know that nanojoules per cubic meter is the same unit as nanopascal which is easier to say. N/m^{2} =Nm/m^{3} = J/m^{3} because a Joule is a Newtonmeter of work.] Take the reciprocal of 16.3, square it, and multiply by 161 nanopascals. That gives you the energy density people think corresponds to the cosmological constant. "16.3^2 * 161 nanopascal" To use the google calculator, paste 16.3^2 * 161 nanopascal into the window. It will do the arithmetic and tell you 6.06 x 10^{10} pascals. Which is 0.606 nanopascal. That, precisely, is the constant energy density which people who imagine there is "dark energy" must think fills all of space. About 3/5 of a nanojoule per cubic meter. But so far, all we have evidence for is a constant curvature term Lambda (the square of a reciprocal length) that appears in the Einstein equation, and improves the fit. 


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