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R(t) for Observable_Today, Universe for early universe ages



 
 
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  #1  
Old December 12th 16, 10:03 PM posted to sci.astro.research
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Default R(t) for Observable_Today, Universe for early universe ages

I want to determine the radius vs time for the universe (observable
today) but using universe ages starting with age =3D 0.721 Gyr and
moving forward in Gyr increments. Ned Wright's calculator gives values
but from our current perspective, looking outward into the surrounding
universe, whereas I want to go back in time and am not sure I can use
the values.

Using the calculator, I got the below values for radius of the universe
as a function of the distance out I look using z values to give Gyr
increments with default settings for co moving radius:

If I did this right, the following are the co moving radii for the
universe out to the same co moving radius (that we see today) applied
to different ages of the universe starting at 0.721Gyr and increasing by
1Gyr per data point up through present at 13.721Gyr. To the same co
moving radius of the universe, the current value is 30.79GLyr, whereas
to that same co moving radius at 0.721Gyr age, the co moving radius
would have been 14.21GLyr if I did this right.

But I used the modern co moving radii, then just multiplied by the ratio
of universe age, and am not sure the inversion is correct....ie, that
the expansion is (I think the term would be) reversible / self similar??

14.214956
14.7706565
15.35837267
15.998686
16.7039454
17.48512767
18.36849871
19.37748225
20.56168078
21.9975072
23.83462436
26.39463033
30.79097946

But it's different to look backward from the present, compared to
looking forward from the past. ie, if we today were in the universe at
age 0.721 Gyrs, would the co moving radius back then have been
14.21Glyr? And today, due to expansion, the co moving radius is now
around 30.8Glyrs.

Not sure this is a legitimate transformation.

rt

  #2  
Old December 12th 16, 11:52 PM posted to sci.astro.research
Phillip Helbig (undress to reply)[_2_]
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Posts: 273
Default R(t) for Observable_Today, Universe for early universe ages

In article ,
writes:

I want to determine the radius vs time for the universe (observable
today) but using universe ages starting with age =3D 0.721 Gyr and
moving forward in Gyr increments. Ned Wright's calculator gives values
but from our current perspective, looking outward into the surrounding
universe, whereas I want to go back in time and am not sure I can use
the values.

Using the calculator, I got the below values for radius of the universe
as a function of the distance out I look using z values to give Gyr
increments with default settings for co moving radius:

If I did this right, the following are the co moving radii for the
universe out to the same co moving radius (that we see today) applied
to different ages of the universe starting at 0.721Gyr and increasing by
1Gyr per data point up through present at 13.721Gyr.


I'm not completely sure what you want. If you take the current radius
of the observable universe (the present proper distance to the particle
horizon---you need to understand all these terms to make progress) and
want to know the distance to an object which is now at the particle
horizon for times in the past (as opposed to the size of the particle
horizon back then; an object at the particle horizon now would, in
general, have been outside it in the past), then that is easy: just
divide by (1+z). Just don't confuse this with the speed of light
multiplied by the lookback time, nor with the luminosity distance, nor
with the angular-size distance, nor with the proper-motion distance, nor
with the parallax distance, nor with the scale factor of the universe.
  #3  
Old December 13th 16, 10:10 PM posted to sci.astro.research
Phillip Helbig (undress to reply)[_2_]
external usenet poster
 
Posts: 273
Default R(t) for Observable_Today, Universe for early universe ages

In article ,
writes:

But I used the modern co moving radii, then just multiplied by the ratio
of universe age, and am not sure the inversion is correct....ie, that
the expansion is (I think the term would be) reversible / self similar??


As I mentioned in another post, if you want what I think you want, just
forget the age and divide the current value by (1+z).

While what you mention above might hold in a special case, it is in
general certainly not true. Consider a universe which, at the
transition between the decelerating and accelerating phases, is almost
static. Yes, this requires fine-tuning of lambda and Omega, but is
possible and illustrates the point. The quasi-static phase can be
arbitrarily long, and the change in redshift (and hence scale factor)
arbitrarily small. So you could have a range in z between, say, 1.999
and 2.000 which corresponds to a trillion years.

Some things are hard, at least in the general case, such as calculating
distances from redshift or vice versa, calculating the scale factor as a
function of time, and so on. In general, these involve elliptic
integrals (or the inverse). On the other hand, some things can be done
with simple algebra. For example, given the current values of lambda
and Omega, it is simple (just based on their definitions) to calculate
the redshift at which they were equal.
 




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