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Look 88 billion years into future with the A20 tabular calculator

by marcus
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Naty1
#19
Jan21-13, 04:26 PM
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None of the columns seem to have the 41 Million light years distance in there.
edit: oops, did not realize we have a page two...and two more posts befoe this. [We shall have to slow Marcus down as in "Curb that enthusiasm." as he is posting faster than I am reading [LOL]....

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....
marcus
#20
Jan21-13, 06:30 PM
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Quote Quote by Naty1 View Post
edit: oops, did not realize we have a page two...and two more posts befoe this. [We shall have to slow Marcus down as in "Curb that enthusiasm." as he is posting faster than I am reading [LOL]....

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....
It's great you are using the calculator, I find it really "empowering" (as they say).

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.
marcus
#21
Jan21-13, 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:


S	a	T	       T_Hub	D_now	D_then	D_hor
1090.0	0.0009	0.000381	0.0006	45.9	0.0421	0.056
981.1	0.0010	0.000455	0.0008	45.8	0.0467	0.063
872.2	0.0011	0.000554	0.0009	45.7	0.0524	0.070
763.3	0.0013	0.000691	0.0011	45.6	0.0598	0.080
654.4	0.0015	0.000889	0.0015	45.5	0.0695	0.093
545.5	0.0018	0.001196	0.0019	45.3	0.0830	0.112
436.6	0.0023	0.001712	0.0027	45.0	0.1032	0.139
327.7	0.0031	0.002704	0.0043	44.7	0.1363	0.184
218.8	0.0046	0.005103	0.0080	44.0	0.2012	0.273
109.9	0.0091	0.014809	0.0227	42.6	0.3875	0.530
1.0	1.0000	13.754712	13.8999	0.0	0.0000	15.622
I checked the calculator's "copy/paste friendly version" box to get a table output in a format that I could copy and paste easily. But the normal output looks better, in the grid designed for it. So try it yourself
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)
Jorrie
#22
Jan21-13, 09:56 PM
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Quote Quote by marcus View Post
The trouble is we have a distribution bottleneck. More beginning astronomy students should get to use it. I don't know how to get the word out. Maybe there are some active academics here at PF who would be willing to pass the link along to colleagues in the astronomy department.
I've got some feedback that our use of the Hubble times Ynow and Yinf as the primary input parameters are off-putting to some teachers. They say it brings in the idea of the Hubble time too early for beginners and they would like to start with the Omegas; students do not find the Y's in published results, only the Omegas. Some also prefer z rather than S as an input, but this is not really an important issue. Maybe having negative z for the future is more intuitive than our 0 < S < 1?

Actually in my calculator I immediately convert the Ys to Omegas, so apart from the user interface and "front-end", nothing else need to change. I will look into the possibility of a B-model, returning it to the legacy input parameters, giving people a choice.

What do you think?
Jorrie
#23
Jan21-13, 10:11 PM
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Quote Quote by Naty1 View Post
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....
Yes, if you look at the equations in http://www.physicsforums.com/showpos...3&postcount=29, they all have integrals - hence the need for a numerical integrator...

(Now CosmoLean_A27, no longer A22).
mfb
#24
Jan22-13, 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.
Jorrie
#25
Jan22-13, 10:15 PM
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Quote Quote by mfb View Post
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.
Yes, good idea. I will look into that as an option during the next update.

What do you think of working with Hubble time inputs vs. standards density parameters and Hubble constant as input?
mfb
#26
Jan23-13, 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.
Jorrie
#27
Jan27-13, 04:19 AM
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Quote Quote by mfb View Post
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.
I have done a first attempt at an optional nonlinear scaling of the stretch (scale) factor. It divides S by any S_step larger than 1, with 2 probably the most useful. There is a tick box in the latest version, which I have renamed to TabCosmoC1 (for Tabular Cosmological Calculator).

After a bit of forum testing and perhaps tuning, we can make it more visible again.
Naty1
#28
Jan27-13, 09:50 AM
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Jorrie...this model: cool. Thanks for your efforts.!!
mfb
#29
Jan27-13, 10:05 AM
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Very nice, thanks.

Yinf standard is 16.3, but the tooltip gives 16.9 as best fit?
marcus
#30
Jan27-13, 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)

S	a	T	T_Hub	D_now	D_then	D_hor
1090.00	0.001	0.000	0.001	45.890	0.042	0.056
768.34	0.001	0.001	0.001	45.617	0.059	0.080
541.61	0.002	0.001	0.002	45.280	0.084	0.112
381.78	0.003	0.002	0.003	44.870	0.118	0.158
269.12	0.004	0.004	0.006	44.373	0.165	0.223
189.70	0.005	0.006	0.010	43.773	0.231	0.313
133.72	0.007	0.011	0.017	43.051	0.322	0.439
94.26	0.011	0.019	0.029	42.186	0.448	0.613
66.44	0.015	0.032	0.049	41.151	0.619	0.855
46.84	0.021	0.054	0.082	39.913	0.852	1.186
33.02	0.030	0.092	0.140	38.436	1.164	1.638
23.27	0.043	0.157	0.236	36.673	1.576	2.248
16.40	0.061	0.265	0.399	34.571	2.107	3.061
11.56	0.086	0.449	0.675	32.066	2.773	4.125
8.15	0.123	0.759	1.140	29.084	3.568	5.486
5.75	0.174	1.282	1.917	25.541	4.445	7.167
4.05	0.247	2.159	3.200	21.353	5.272	9.133
2.86	0.350	3.607	5.224	16.474	5.770	11.247
2.01	0.497	5.913	8.091	10.988	5.460	13.230
1.42	0.705	9.312	11.326	5.272	3.716	14.739
1.00	1.000	13.755	13.900	0.000	0.000	15.622
0.70	1.419	18.895	15.324	-4.341	-6.158	16.025
0.50	2.013	24.378	15.937	-7.598	-15.292	16.178
0.35	2.855	29.998	16.170	-9.954	-28.419	16.225
0.25	4.050	35.670	16.254	-11.630	-47.105	16.254
0.17	5.746	41.360	16.284	-12.816	-73.637	16.284
Jorrie
#31
Jan27-13, 01:48 PM
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Quote Quote by mfb View Post
Yinf standard is 16.3, but the tooltip gives 16.9 as best fit?
Yes, tooltip in error. Thanks for heads-up, will fix.
Jorrie
#32
Jan27-13, 01:59 PM
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Quote Quote by marcus View Post
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
I thought about putting something like this in the calculator, but in order to retain flexibility, it clutters the relatively 'clean' look and feel a little. Maybe I should put it in the accompanying tooltip...

Edit: Done. Also fixed the tooltip mistake.

If your cache prevents modified version from loading, try TabCosmoC2.html. It is the same as C1.
marcus
#33
Jan31-13, 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 about--that 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 years---this 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 faster---around 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.


S	a	T	T_Hub	D_now	D_then	D_hor
1090.0	0.001	0.00038	0.001	45.890	0.042	0.056
863.33	0.001	0.00056	0.001	45.714	0.053	0.071
683.80	0.001	0.00083	0.001	45.512	0.067	0.089
541.60	0.002	0.00121	0.002	45.280	0.084	0.112
428.97	0.002	0.00176	0.003	45.016	0.105	0.141
339.77	0.003	0.00255	0.004	44.715	0.132	0.178
269.11	0.004	0.00369	0.006	44.373	0.165	0.223
213.15	0.005	0.00532	0.008	43.985	0.206	0.280
168.82	0.006	0.00764	0.012	43.547	0.258	0.351
133.72	0.007	0.01095	0.017	43.051	0.322	0.439
105.91	0.009	0.01567	0.024	42.492	0.401	0.549
83.889	0.012	0.02239	0.034	41.861	0.499	0.685
66.444	0.015	0.03196	0.049	41.151	0.619	0.855
52.627	0.019	0.04555	0.069	40.350	0.767	1.064
41.683	0.024	0.06488	0.098	39.449	0.946	1.322
33.015	0.030	0.09233	0.140	38.436	1.164	1.638
26.150	0.038	0.13132	0.198	37.295	1.426	2.024
20.712	0.048	0.18667	0.281	36.013	1.739	2.494
16.405	0.061	0.26525	0.399	34.571	2.107	3.061
12.993	0.077	0.37676	0.567	32.950	2.536	3.739
10.291	0.097	0.53495	0.804	31.129	3.025	4.544
8.151	0.123	0.75926	1.140	29.084	3.568	5.486
6.456	0.155	1.07696	1.613	26.790	4.149	6.571
5.114	0.196	1.52614	2.277	24.220	4.736	7.794
4.050	0.247	2.15887	3.200	21.353	5.272	9.133
3.208	0.312	3.04392	4.454	18.176	5.666	10.540
2.541	0.394	4.26571	6.093	14.701	5.786	11.940
2.013	0.497	5.91316	8.091	10.988	5.460	13.230
1.594	0.627	8.05254	10.269	7.165	4.495	14.305
1.263	0.792	10.6898	12.304	3.428	2.715	15.101
1.000	1.000	13.7547	13.900	0.000	0.000	15.622
0.792	1.263	17.1291	14.965	-3.021	-3.814	15.929
0.627	1.594	20.6981	15.594	-5.540	-8.831	16.095
0.497	2.013	24.3777	15.937	-7.598	-15.292	16.178
0.394	2.541	28.1165	16.117	-9.255	-23.516	16.216
0.312	3.208	31.8857	16.208	-10.578	-33.934	16.230
0.247	4.050	35.6702	16.254	-11.630	-47.105	16.254
0.196	5.114	39.4625	16.277	-12.465	-63.743	16.277
0.155	6.456	43.2586	16.289	-13.127	-84.754	16.289
0.123	8.151	47.0568	16.294	-13.652	-111.28	16.294
0.097	10.291	50.8558	16.297	-14.068	-144.77	16.297
0.077	12.993	54.6553	16.299	-14.397	-187.06	16.299
0.061	16.405	58.4551	16.299	-14.658	-240.46	16.299
0.048	20.712	62.2551	16.300	-14.865	-307.87	16.300

Time now (at S=1) or present age in billion years:	13.7547
Again looking at the bottom row, to give an example of telling yourself stories to interpret the numbers, suppose today we decide to send a message (an intense flash of light) to a galaxy which is NOW 14.865 billion LY from us. there are lots of galaxies like that, most of those we see with a telescope are that far or farther. So imagine we pick out an especially pretty one and decide to send them a message today. How long will the message take to reach them? Well today is year 13.75 billion and the table says the message gets there in year 62.25 billion, so you do the arithmetic.
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.einsteins-theory-of-relat...abCosmoC1.html
As always, thanks Jorrie. It's neat.
marcus
#34
Feb1-13, 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 16.3---you 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.
Naty1
#35
Feb2-13, 08:30 AM
P: 5,632
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!!
marcus
#36
Feb2-13, 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: 13.92/16.32 = .73

13.9 billion years is information about the present, it is 1/Ho 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/m2 =Nm/m3 = J/m3 because a Joule is a Newton-meter 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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