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# Astrophysics/Temperature of the cosmic radiation

Question
Hi,
The notes are :
As the Universe expands, the space temperature decreases linearly because the photons lose energy to gravitational redshift. The formula that links the temperature with the red shift is T(t) = T(0)*(1 + z), where T(t) is the temperature at time t (backward in time) and T(0) is the one to 'current era (2,7K). In fact, at the time of recombination, that is, when the universe was 380 thousand years, the temperature was 3000K: If you replace the formula in the redshift of the time, ie z = 1100, you get exactly 3000K. As for the future, we should replace negative values ​​in the formula so if the redshift z = 0.5 we have that T (t) = 1,35K which roughly corresponds to a period of about 5 billion years, but it depends the cosmological model, and if we assume a rate of growth to determine the so-called lookbacktime.
In another way, we can correlate the variation of redshift and time according to the formula (1 + z) proportional to 1 / t (2/3), where it intends to t (which is the time) raised to the 2/3. We see that as t tends to 0, the temperature becomes infinite, while for t tends to infinity, the temperature tends to 0 Let's say that the temperature of the space will reach absolute zero hypothesis of the Big Freeze, that is, when asymptotically the value of the redshift z tends to zero.

Questions:
1) With the formula T(t) = T(0)*(1 + z) I get T(t) 2.7 * (1100 + 1)
2.7 * 1101 = 2972 which is in good agreement with the 3000 degrees Kelvin above.
But my concern is that I would never have thought that there could be a
such high redshift (1100) .When have been sighted (I think with Hubble
the most distant galaxies, it seems to me that there was talk of a redshift 10.
It 's all right or is there something wrong?

2) As for the future, we should replace in the formula negative values ​​of redshift z = -0.5, therefore, if we have that T (t) = 1,35K which roughly corresponds to a period of about 5 billion years. ..
What does it mean: a period equal to about 5 billion years ... starting today, the temperature dropping to 1.35 K would take 5 billion years?

3) In another way, we can correlate the variation of redshift and time according to the formula (1 + z) proportional to 1 / t (2/3), where it intends to t (which is the time) raised to the 2/3 . We see that as t tends to 0, the temperature becomes infinite, while for t tends to infinity, the temperature tends to 0.
Of this other formula did not understand much ... maybe if someone could give an example with the little numbers would be more clear.
Antonella

You keep changing the name under which you ask questions.  For consistency and understanding, please don't do that.

Unfortunately, you're putting in redshift values for a lot of this which don't actually make sense.  Redshift is a quantity which you can observe and measure, and which depends on the relative velocity (when the light was emitted) of the thing which you are measuring and observing.  For the CMBR (when it decoupled), it's for the period of recombination, and not for galactic formation (which took significantly longer).  Each galaxy has its own redshift, depending on how fast it is receding from us.  You can't just "stick in" a redshift of 0.5.  If I want a redshift of 0.5, all I have to do is look at something closer to me.  Just sticking in a value of z for the CMBR does not make sense.  It is what it is, not what we put into a formula.  To your questions:
1) Galaxies took a very long time to form.  The solar systems took a long time to form.  The stars don't just "slow down" right away and form whirlpools.  Billions of years (google search "dark ages of the universe" and you'll get a ton of references) went by before the furthest galaxies started emitting visible light.  Those are closer to us, and at lower redshift.
2)  Simply replacing values of z for redshift means nothing, not if you understand how the formula was derived.  It was derived for a specific redshift at a specific time.  Recombination happened at a specific time, corresponding to a specific redshift.  You can't just replace it and have it make sense in the same context.
3)  See 2.

Astrophysics

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#### Dr. Stephen O. Nelson

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