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m1omg
2009-Jan-21, 07:14 PM
I found a very approximate formula for calculating CMB temperature based on the age of the universe; 10 to the 10th power/square root of the age of the universe in seconds but it is VERY approximate; the temperature of current universe comes off as around 15 K, what is the formula for a bit more precise calculation?

It still is useful for ballpark approximate order of magnitude calculations through, I even did a little list for the ages and the approx. order of magnitude of temperature;

a shortest blink of an eye after the Big Bang = 0.005 s = cca 10-100 billion K

1 hour after the BB = cca 100 million K
10 years after the BB = cca 1 million K
100 years ABB = 100 thousand K
1000 years ABB = 10-100 thousand K
10 000 years ABB = 10 000 K
100 000 years ABB = 1000-10 000 K
1 million yrs. ABB = 1000 K
100 million years. ABB = 100 K
1 billion years ABB = 10 K

... (intermediate dates ommited due to inacurracies)

10 to the 14th power yrs. ABB (star formation from gas clouds stops) = cca 0.1 K

10 to the 15th power yrs. ABB (all stars formed from gas clouds [not from brown and white dwarf collisimns] have stopped fusing, most planets detached from orbits by stars passing close) = 0.01 K

10 to the 19th power yrs. ABB (low estimate until most of the stellar remnants and brown dwarfs are ejected from galaxies, the rest remain near the center and later they are consumed by the central BH where they spiral due to grav. radiation) = >0.0001<0.0009 K

10 to the 20th power yrs. ABB (high estimate until most of the stellar remnants and brown dwarfs are ejected from galaxies, the rest remain near the center and later they are consumed by the central BH where they spiral due to grav. radiation, Earth falls on the Sun because of grav. rad. if not ejected from the Solar system before) = still around 0.0001 K

10 to the 27th power yrs. ABB = the middle of the Degenerate Era = 0.00000001 K

10 to the 32th power yrs. ABB = proton decay begins = 10 to the -10th power K

10 to the 37th power yrs. ABB = half the protons are decayed = 10 to the -13th power K

10 to the 40th power yrs. ABB = all protons gone, Black hole Era begins = 10 to the -14th power K

10 to the 70th power yrs. ABB = the middle of the BH era = 10 to the -29th power K

10 to the 100th power yrs. ABB = Dark Era begins, all realistic BHs are evaporated now, the universe is almost totally dead, only photons and elementary particles remain now, positronium atoms about the diameter of the current universe can form, almost total heat death = 10 to the -44th power K, EDIT - I have read some things on this and is seems that there would be actually some interesting things occuring in the universe in this far future, we just cannot extrapolate so much yet

It should be noted that these are all crude order of magnitude data and if there is interval like 10 000-100 000 K, it does not mean great variations in temperature but uncertainity with even the order of magnitude.

Tzarkoth
2009-Jan-22, 01:29 PM
positronium atoms about the diameter of the current universe can form,

I'm not sure what you mean here?

I believe the exact calculations can be found here,

http://www.astro.uu.se/~nisse/courses/kos2006/lnotes/ln6.pdf

m1omg
2009-Jan-22, 03:30 PM
I'm not sure what you mean here?

I believe the exact calculations can be found here,

http://www.astro.uu.se/~nisse/courses/kos2006/lnotes/ln6.pdf

Thanks but I haven't found that formula there, just formulas about when the matter and radiation density was equal etc.
About the positronium;

http://en.wikipedia.org/wiki/Positronium
http://en.wikipedia.org/wiki/Dark_Era#Dark_Era
http://209.85.129.132/search?q=cache:ZUt3HDuGCSgJ:search.barnesandnoble. com/The-Five-Ages-of-the-Universe/Fred-C-Adams/e/9780684865768+giant+positronium+dark+era+cosmology&hl=sk&ct=clnk&cd=6&client=safari

Tim Thompson
2009-Jan-23, 06:30 AM
There is no formula for calculating the temperature of the universe from first principles. You have to specify a particular cosmological model and work it out the hard way. However, given the temperature now (T0 = 2.728 Kelvins) you can calculate the temperature of the CMB (the radiation temperature) as a function of redshift: T = T0(1+z) where z is the redshift. The average nonrelativistic gas temperature as a function of redshift is almost the same, T = T0(1+z)2. See Cosmology: The Science of the Universe by Edward Harrison; Cambridge University Press, 2000 (2nd ed.) page 346.

Tom Mazanec
2014-Jan-02, 04:15 PM
This is interesting, but how do I calculate what the temperature will be in the year, say, 100 billion or 1 trillion?

ngc3314
2014-Jan-02, 10:33 PM
If you have a cosmological model that you believe which relates redshift to lookback time, the CMB temperature observed at a particular epoch scales as (1+z) where z is the redshift we observe at the epoch in question. (To extrapolate forward, z becomes negative - in a quick check, for example, Ned Wright's JavaScript calculator (http://www.astro.ucla.edu/~wright/CosmoCalc.html) gives results that look reasonable for negative z, but no guarantee that it's set up to trap those in a physical helpful way)