From Aeon to Zeon to Zeit, simplifying the standard cosmic model

In summary, the universe is expanding at a rate that is 20% larger than the eventual constant rate. The present age of the universe is 0.8 zeons.
  • #246
Hi, I just got back. The errand was more work than I thought.
Before I forget it, I will say a problem that came to mind while I was out. I am still learning how to think up cosmology quiz questions.

In ancient times there was a race of giant stars called "PopIII" stars. The name is an historical accident and meaningless. They lived when distances were about a TENTH the present size. These stars are very interesting because they formed before there were heavier elements---they were made of H and He (with traces of Li) and their light had the wavelengths of hot H and He but not other gases.

It is very hard to find the small protogalaxies or regions with these PopIII stars. They were 100 to 1000 more massive than Sun and so burned very hot and had short lives. Sometimes astronomers have detected these ancient stars. How far away is the matter which once formed them?
Of course they are no longer. The actual stars exploded in SNe long ago, but the matter is still there, that made the light.

Suppose you are an astronomer who is just now getting some S=10 light from a region with these giant stars. How far away is that?
 
Last edited:
  • Like
Likes RyanH42
Space news on Phys.org
  • #247
RyanH42 said:
...

And also I checked my answer to use lightcone(Which I learned I guess) and it seems my answer is true.
: ^) Yes it seems it is.
 
  • Like
Likes RyanH42
  • #248
D(t)=-∫dS/H integral between 1 and 10
H=[(S/1.3)^3+1]^(1/2) so the answer is 1.7564
 
  • #249
Great story
 
  • #250
I just had lunch. It is getting near 3pm pacific when you end the day, I think. There may be no more time. until tomorrow.
Here is a quick variation on an earlier problem.

You are transported to some unknown place and time in the future. You measure and find that the CMB is HALF the temperature it is today.
What time is it?

By an amazing coincidence, while you are listening to the radio you receive a message that was sent by us at PF today. What distance are you from Earth?
 
  • #251
First qustion answer
We are in the future that's certain.So Let's call the time T.In this time we measure the CMB and we saw that it was half of its tempature today(Here we can use Wien Law Half of tempature means 2 times wavelenght .Then the equation becomes ##2=a(T)/a(t_0)##
So ##2=a(T)/1.3##
##a(T)=2.6## then what will be T sinh(1.5T)^(2/3)=2.6
sinh(1.5T)=2.6^(3/2)
##sinh(1.5T)=4.19237##
##T=1.427## zeit

If I find a better solution I will going to write it
 
Last edited:
  • #252
D(1.427)=∫dtsinh(1.5*1.427)^(2/3)/sinh(1.5*t)^(2/3) integral 0.8 to 1.427
1.301 lightzeit
 
Last edited:
  • #253
I didnt underatand first and second question is related first.And I can assure you I have never checked what we did before (The equations).If my answers are true then I am certain that you teach me.
 
  • #254
RyanH42 said:
First qustion answer
We are in the future that's certain.So Let's call the time T.In this time we measure the CMB and we saw that it was half of its tempature today(Here we can use Wien Law Half of tempature means 2 times wavelenght .Then the equation becomes ##2=a(T)/a(t_0)##
So ##2=a(T)/1.3##
##a(T)=2.6## then what will be T sinh(1.5T)^(2/3)=2.6
sinh(1.5T)=2.6^(3/2)
##sinh(1.5T)=4.19237##
##T=1.427## zeit
...
This is correct.
Remember that we are using approximations---for the present I am always saying 0.8 instead of 0.797. And I use the approximation 1.3
instead of something like 1.3115...
So our answers will not agree exactly with Jorrie's calculator
Here I put in Supper = .5 and number of steps = 0 (just to get one row of the table) and selected Dnow
[tex]{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (zeit)&D_{now} (lzeit)&D_{then}(lzeit) \\ \hline 2.000&0.500&1.435182&0.457231&0.914463\\ \hline \end{array}}[/tex]

So you were transported to a time 1.435 (and we got 1.427 which is close enough since we use approximations like 0.8 for the present.
And you landed on a planet which is NOW 0.457 lightzeit from us.
But it is at a time when distances are TWICE what they are now, so that planet is then 0.914 lightzeit from us.

For the second part you should get around 0.9 lightzeit---because it is an approximation anything near to 0.9 is good. and you showed the correct integral in your answer (but for some reason there was a numerical error.)

If you do the integral again, that you wrote, I think you would get about 0.89 which is close to 0.9.
 
Last edited:
  • #255
RyanH42 said:
D(1.427)=∫dtsinh(1.5*1.427)^(2/3)/sinh(1.5*t)^(2/3) integral 0.8 to 1.427
...
I tried sinh(1.5*1.427)^(2/3)/sinh(1.5*t)^(2/3) integral 0.8 to 1.427 in numberempire
and got 0.89
 
  • #256
Actually my second part is also true.But I made a little mistake If you put this equation into numberempire you get close to 0.89 (If you put the sinh(1.5*1.427)^(2/3)/sinh(1.5*t)^(2/3))
Its close to 0.9 cause there's some erros as you said.
But I put numberempire
sinh(1.5*1.8)^(2/3)/sinh(1.5*t)^(2/3)
Which the reason why I get 1.3.
I made copy one of the equations which we write here and I am changing the numbers so I forget to change that number.If you put my equation in #252 you will get a close answer(due to some errors)
 
Last edited:
  • #257
I see! I often do that and make the same typo error. I copy-paste something to save typing and then forget to change one of the numbers in it. : ^)
 
  • Like
Likes RyanH42
  • #258
"typo" is short for "typographical error". It's when you know the right thing but type it wrong. Everybody makes typos. I'm impressed by your good answers. Also putting in Wien's Law. I'm happy.

We don't need to go further right now, but I will lay out one or two ideas that we could advance to when you feel like it. there is no hurry. there is the "(cosmic) event horizon" and the "particle horizon"
they are easy to calculate with what you have now, and they are standard cosmology concepts.
 
Last edited:
  • #259
Oh,I know and good morning :)
 
  • #260
And good afternoon to you :^)
 
  • Like
Likes RyanH42
  • #261
Let's try integrating that same thing but changed to give the disgtance now sinh(1.5*0.8)^(2/3)/sinh(1.5*t)^(2/3) integral 0.8 to 1.427 in numberempire
 
  • #262
0.454
 
  • #263
that gives the distance now, to a galaxy which I could send a signal to today which would get there at time t = 1.427

now let's change that time to infinity
in numberempire you can write "inf" to get the integral out to infinity (the 4th example on their page shows this)

I think this will give me the distance NOW to the farthest galaxy my signal (which I send today) can ever reach. (I make 1.427 very large, in other words)
 
  • #264
I can't write infinity.It makes error in calculator.

I am typing to use my phone.So I am a bit slow
 
  • #265
I get an error too! I can integrate to 100, and 200 but not to 500!
I see that it is approaching a limit, because it changes very little between 100 and 200

So I was wrong. We cannot simply put "inf" into numberempire and get the integral to infinity.
Numberempire is disappointing me in that respect.

Let's see if we can do it this way

$$D(S) = \int_S^1 ((s/1.3)^3 + 1)^{-1/2}ds$$

Maybe I should get a second cup of coffee first.
 
Last edited:
  • Like
Likes RyanH42
  • #266
Probably yeah we need another calculater. I will try Symbolab
 
  • #267
No result in Symbolab
 
  • #268
Wait! it is all right.
I integrate ((s/1.3)^3+1)^(-1/2) from 0.001 to 1 and I get the right thing. D = 0.9508

Let me try from 0 to 1
Yes. It gives 0.952this is the cosmic event horizon. It is the distance now of the farthest galaxy I can reach with a signal I send today
and the distance now of the farthest that can ever have a causal effect on us by what happens there today.
beyond that horizon, no signal they send today can ever reach us

$$ \int_0^1 ((s/1.3)^3 + 1)^{-1/2}ds$$

[tex]{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (zeit)&D_{now} (lzeit)&D_{then}(lzeit)&D_{hor}(lzeit) \\ \hline 1.000&1.000&0.796948&0.000000&0.000000&0.952155\\ \hline \end{array}}[/tex]
 
Last edited:
  • Like
Likes RyanH42
  • #269
I have some problems with my mom
She thinks I am spending a lots of time in phone but that's not true.I am talking with you and I am learning something .

Anyway I understand that.If we send a signal now that signal can go further a galaxy which 0.952 lightzeit distance from us.And also that's true for who lives that galaxy.So If I send I am here signal thus signal will reach anywhere but not beyond the 0.952 lightzeit.
 
  • #270
It seems like you understand the cosmic event horizon idea!
Maybe I will do some other things for an hour or two. It's good to keep the Mom happy and it's good to get exercise and do real world things
 
  • #271
Ok.I am in holiday and here there's really nothing to do.Nothing
 
  • #272
I am guessing that your time zone is near UTC or european central. It is 8am pacific, so maybe where you live is 16h, or 4pm? or maybe 5 pm?
I don;t have anything I need to do for the next 2 hours.
We could take up another standard concept---the "particle horizon".
but I want your Mom to be happy.
 
  • #273
S=0 means infinty isn't it.I means S=1/a(t) If a(t) goes infinity S goes zero.
 
  • #274
Yes that's right, it is just another way to do the same integral, but without having to say "sinh"
Real world human relationships are obviously very very important. Please ignore what I say about particle horizon if there is a risk of making your mother unhappy. Any of this "horizon" business can wait till tomorrow or another day.

Let's try
((s/1.3)^3+1)^(-1/2) between 1 and inf
That is going back in time, from the present, back to very early (large S)

Yes! that works. That gives what cosmologists call the present "radius of the observable universe"
You can see it is 2.69.

It is the distance from us NOW of the farthest matter which could have sent us a signal, some light, some neutrinos, some gravity waves, anything, which is arriving today.

this distance is also called "particle horizon" because it is the farthest distance any particle can have traveled (helped by expansion) starting at the earliest time, at the beginning of expansion.

[tex]{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (zeit)&D_{now} (lzeit)&D_{then}(lzeit)&D_{hor}(lzeit)&D_{par}(lzeit) \\ \hline 1.000&1.000&0.796948&0.000000&0.000000&0.952155&2.675083\\ \hline \end{array}}[/tex]
 
Last edited:
  • #275
Yes We can do
 
  • #276
The problem is am a shy person .I don't have any friends.
 
  • #277
Ok.Lets do this not today.Maybe tomorrow.You can write what you need to write (so you can ready to teach me)
 
  • #278
Tomorrow is good. I live at the edge of the city near some open country, and some hills with only trees, grass, birds, deer,...
I walk.
It is good exercise. I sometimes get my neighbors to walk with me. It is easy to be with them when we are walking in Nature. looking at the sky and the hills, and the water. The purpose is to get some exercise. The neighbor knows it is for her good health or his good health. So there is a purpose to going on the walk. Either alone or with a companion. I will go walking this morning, with a neighbor who is a retired university professor. She used to teach language, or linguistics. It is an easy way to be with people, when there is a purpose, and a natural environment.
 
  • Like
Likes RyanH42
<h2>1. What is the standard cosmic model?</h2><p>The standard cosmic model is a scientific theory that describes the evolution of the universe from its initial state to its current form. It is based on the Big Bang theory, which states that the universe began as a singularity and has been expanding ever since.</p><h2>2. What is Aeon, Zeon, and Zeit in the context of the cosmic model?</h2><p>Aeon, Zeon, and Zeit are hypothetical eras in the standard cosmic model that represent different stages of the universe's evolution. Aeon refers to the period of inflation, Zeon represents the radiation-dominated era, and Zeit corresponds to the matter-dominated era.</p><h2>3. How does the standard cosmic model explain the formation of galaxies and other structures?</h2><p>The standard cosmic model proposes that after the Big Bang, small fluctuations in the density of matter led to the formation of clumps of matter, which eventually grew into galaxies and other structures through the force of gravity.</p><h2>4. What evidence supports the standard cosmic model?</h2><p>There is a significant amount of evidence that supports the standard cosmic model, including the cosmic microwave background radiation, the abundance of light elements, and the large-scale structure of the universe. These observations are consistent with the predictions of the model.</p><h2>5. Are there any alternative theories to the standard cosmic model?</h2><p>Yes, there are alternative theories to the standard cosmic model, such as the steady-state theory and the cyclic model. However, these theories are not as widely accepted as the standard cosmic model and do not have as much evidence to support them.</p>

1. What is the standard cosmic model?

The standard cosmic model is a scientific theory that describes the evolution of the universe from its initial state to its current form. It is based on the Big Bang theory, which states that the universe began as a singularity and has been expanding ever since.

2. What is Aeon, Zeon, and Zeit in the context of the cosmic model?

Aeon, Zeon, and Zeit are hypothetical eras in the standard cosmic model that represent different stages of the universe's evolution. Aeon refers to the period of inflation, Zeon represents the radiation-dominated era, and Zeit corresponds to the matter-dominated era.

3. How does the standard cosmic model explain the formation of galaxies and other structures?

The standard cosmic model proposes that after the Big Bang, small fluctuations in the density of matter led to the formation of clumps of matter, which eventually grew into galaxies and other structures through the force of gravity.

4. What evidence supports the standard cosmic model?

There is a significant amount of evidence that supports the standard cosmic model, including the cosmic microwave background radiation, the abundance of light elements, and the large-scale structure of the universe. These observations are consistent with the predictions of the model.

5. Are there any alternative theories to the standard cosmic model?

Yes, there are alternative theories to the standard cosmic model, such as the steady-state theory and the cyclic model. However, these theories are not as widely accepted as the standard cosmic model and do not have as much evidence to support them.

Similar threads

Replies
6
Views
1K
Replies
34
Views
2K
  • Calculus and Beyond Homework Help
Replies
13
Views
1K
Replies
13
Views
1K
Replies
6
Views
2K
Replies
9
Views
1K
Replies
5
Views
874
Replies
9
Views
1K
Replies
7
Views
2K
  • Cosmology
Replies
11
Views
1K
Back
Top