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Increase in size of universe over past billion years?



 
 
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  #1  
Old September 19th 16, 06:00 PM posted to sci.astro.research
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Default Increase in size of universe over past billion years?

I'll try to pose this well enough to enable an answer. I'll assume
13.7E9 light years radial extent today, ie, 13.7E9 year old universe
for discussion.

Then:

1) 1 billion years ago, the universe was 12.7E9 light years radius,
and years old.

2) We could at that time see the CBR, though it would be hotter
than it is today.

3) The gas that lies within the universe at that time had just
entered the "dark ages" prior to star formation.

4) Today, that gas is seen as 1 billion year old infant galaxies,
which formed over those billion years.

Question:

If I measured the volume of the universe a billion years ago, inside
of the CBR...........and then I repeated that measurement today but
only out to that same gas, which are now galaxies, what would the
increase in volume of the universe be?

I have the Hubble flow so could apply that. But I take it that the
Dark Energy problem means that I would get a larger value than I
would get by just using the Hubble flow. Is the difference trivial,
or most of the problem? What is the increase in volume............could
just answer per cubic megaparsec I suppose? I'm trying to understand
how Dark Energy changes things.

Said otherwise: What would the volume increase be due to Hubble
expansion of universe, what would it be accounting for Dark Energy
acceleration to the Hubble flow, and what is the delta volume change
for the universe?

Ross Tessien

[[Mod. note -- You might find it useful to look through the superb
textbook
"Edward R. Harrison"
"Cosmology: The Science of the Universe"
Cambridge University Press
1st edition 1981
there is a 2nd edition but I don't have the year handy
-- jt]]
  #2  
Old September 19th 16, 10:50 PM posted to sci.astro.research
Phillip Helbig
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Posts: 38
Default Increase in size of universe over past billion years?

In article ,
writes:

I'll try to pose this well enough to enable an answer. I'll assume
13.7E9 light years radial extent today, ie, 13.7E9 year old universe
for discussion.


This is wrong right off of the bat. Yes, you can trivially measure the
radius of the universe in units of light-travel time, but this is
usually not a useful distance. The proper distance---what most people
probably think of as distance---is much larger. Why? Because the
universe is expanding. Yes, it's complicated, but covered in most
cosmology textbooks.

If I measured the volume of the universe a billion years ago,


I think you mean "a billion years after the big bang".

inside
of the CBR...........and then I repeated that measurement today but
only out to that same gas, which are now galaxies, what would the
increase in volume of the universe be?


Easy: (1+z)^3 times the volume at the redshift of z.

I have the Hubble flow so could apply that. But I take it that the
Dark Energy problem means that I would get a larger value than I
would get by just using the Hubble flow.


I guess you mean that accelerated expansion means that the universe
expands more in the same time than if there is no acceleration so, yes.

Is the difference trivial,


Trivial to calculate.

or most of the problem?


What problem?

What is the increase in volume............could
just answer per cubic megaparsec I suppose? I'm trying to understand
how Dark Energy changes things.


It changes the form of R(t), the scale factor as a function of time.

Said otherwise: What would the volume increase be due to Hubble
expansion of universe, what would it be accounting for Dark Energy
acceleration to the Hubble flow, and what is the delta volume change
for the universe?


Figure out how to calculate distances and volumes as a function of
redshift, then plug things in, assuming some cosmological model.

[[Mod. note -- You might find it useful to look through the superb
textbook
"Edward R. Harrison"
"Cosmology: The Science of the Universe"
Cambridge University Press
1st edition 1981
there is a 2nd edition but I don't have the year handy
-- jt]]


EVERYONE interested in cosmology should read this. The second edition
is from 2000 or so. For the basic stuff here, the first edition is
fine. The second edition has some additional chapters, rather than
(appreciably) changing the old ones.

First things first. The concept of distances (and hence volumes) in
cosmology can be tricky. Let me recommend one of my own papers:

http://www.astro.multivax.de:8000/he...fo/angsiz.html

There are many aspects to this paper, but one of them is pedagogical and
one involves explicit calculations. You need to understand the concept
of cosmological distances first, before trying to solve problems (which
might not even be problems) which depend on them.

  #3  
Old September 21st 16, 10:21 PM posted to sci.astro.research
[email protected]
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Posts: 35
Default Increase in size of universe over past billion years?

Thank you for the thoughts and suggestions. One thing to note is that
while I am not a very good mathematician, I do my best to be precise.

If I say, "a billion years ago" I mean, 1.0E9 years ago.

Let me try again.I know this question is complicated and an answer might
not be easy or maybe not even realistic. I'll take best guesses.

I am trying to put a number to the increase in volume of the universe.

A= Delta V With Dark Energy (includes acceleration)
B= Delta V Without Dark Energy (if expansion was flat, no acceleration
or deceleration)
C = A - B

I seek A and B and C

And also, I need to know the number of stars within the region A (and
assume the number is the same in region B)

Dark Energy is more at work in modern universe, so, using a volume of
say 2 billion light years radial distance from earth would be awesome.

Is this possible to answer........ie, is there a way I can get the
values A,B,C for some large number of stars in the universe?

Thanks,

Ross Tessien

  #5  
Old October 10th 16, 01:48 AM posted to sci.astro.research
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Default Increase in size of universe over past billion years?

On Thursday, October 6, 2016 at 1:06:19 PM UTC-7, Steve Willner wrote:

ross.tessien writes:
I am trying to put a number to the increase in volume of the universe.



The scale factor relative to its present value is always (1+z). The
problem is to calculate time as a function of z or vice versa. That
depends on the cosmological model. I suggest you have a look at Ned
Wright's cosmology calculator at
http://www.astro.ucla.edu/~wright/CosmoCalc.html
and especially at its documentation.
Steve Willner


Thanks Steve,

I used the calculator (hopefully did so correctly). Plugged in
values for z so that I found co moving volume and radius for each
Gyr into the past back to 13Gyr....see table below if it comes
through.

question is: Do these values include the Dark Energy
effect....acceleration to the expansion of the universe?

Also, what parameter would I change so that there is NO Dark Energy
effect and the expansion is solely due to the Hubble flow?

Would I just click on the "Flat" button at the same z values?

Thanks,
Ross

I used default values:
H_o = 69.6
Omega_M = 0.286
Omega_vac = 0.714
and pushed the "General" Button

Look Co
Universe Back Moving
Age Time Volume
z Gyr Gyr Gpc^3
0.075 12.721 1 0.134
0.15885 11.721 2 1.205
0.2534 10.721 3 4.571
0.3616 9.721 4 12.252
0.4873 8.721 5 27.232
0.6363 7.721 6 53.97
0.8178 6.721 7 99.348
1.0462 5.721 8 174.105
1.3474 4.721 9 296.192
1.7715 3.721 10 497.486
2.434 2.721 11 842.187
3.677 1.721 12 1484.868
7.368 0.721 13 2997.275
  #6  
Old October 14th 16, 11:21 PM posted to sci.astro.research
Steve Willner
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Posts: 1,172
Default Increase in size of universe over past billion years?

Ned Wright's cosmology calculator at
http://www.astro.ucla.edu/~wright/CosmoCalc.html


In article ,
writes:
question is: Do these values include the Dark Energy
effect....acceleration to the expansion of the universe?


Did you read and understand the documentation? That's more important
than the numerical values.

What Ned labels Omega_vac is the dark energy parameter (often labeled
Omega_lambda elsewhere). By clicking on "Flat," you are forcing
Omega_vac to be equal to (1 - Omega_M), which is the condition for a
flat universe.

Also, what parameter would I change so that there is NO Dark Energy
effect and the expansion is solely due to the Hubble flow?


If you want zero dark energy, you either have to make Omega_M = 1,
which violates nucleosynthesis constraints by producing too much
deuterium and helium, or you have to accept a non-flat universe,
which violates CMB constraints. If you want to calculate these
models anyway, for the first, set Omega_M = 1 and click "Flat." For
the second, leave Omega_M at 0.286 (or your own favorite value), set
Omega_vac to 0, and click "General." Don't the instructions explain
these steps?

Ned's default values have Omega_M + Omega_vac = 1, so Flat and
General produce identical results.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

 




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