At which time did the CMB become dark?

[Gerinski]

At the time the CMB was emitted it was a glowing yellowish-white radiation at 3000 K. From there as space expanded it became redder and redder eventually falling into what for humans is non-visible infrared.
At which age of the universe did the CMB background turn from red to infrared?
Thanks

 

[Q.B.]

To estimate this, you need to know:
-the dependence of the temperature $T$ of the CMB with time/scale factor $a$ of the universe, which is roughly $T \propto \frac{1}{a}$
-the evolution of the scale factor with time, from the Friedman equation which gives for a matter-dominated universe $\frac{a}{a_0}=(\frac{t}{t_0})^{2/3}$
Then you can get the $t$ you look for by choosing the temperature you want in the following equation: $t = t_0(\frac{T_0}{T})^{3/2}$ where $t_0$ would be present time (13.8 billion years) and $T_0$ would be the present temperature of the CMB, 2.73 Kelvin degrees.

 

[mfb]

There is no hard threshold, it just got darker over time. Based on those arbitrary categories, thermal radiation becomes visible somewhere around 525°C, or ~800 K. Today the temperature is 2.7 K, so we are talking about z=300. Based on this cosmology calculator, this was around 3 million years after the Big Bang.

"Cherry red" at 1000 K corresponds to z=370, 2.2 million years after the Big Bang.

 

[Gerinski]

Thanks a lot.

 

[Chronos]

Photons do not play well in plasma, largely due to a phenomenon known as Compton scattering. This same effect makes it difficult to see anything below the atmosphere of a star. For futher discussion, see; https://ned.ipac.caltech.edu/level5/Sept05/Gawiser2/Gawiser1.html, ORIGIN OF THE COSMIC BACKGROUND RADIATION.

 

[mfb]

Photons do not play well in plasma, largely due to a phenomenon known as Compton scattering. This same effect makes it difficult to see anything below the atmosphere of a star. For futher discussion, see; https://ned.ipac.caltech.edu/level5/Sept05/Gawiser2/Gawiser1.html, ORIGIN OF THE COSMIC BACKGROUND RADIATION.

Everything discussed in this thread happened after the plasma recombined enough to make scattering negligible. That is the whole point of the CMB. The hydrogen got re-ionized much later (>100 million years), but at that time it was so spread out that it didn't make the universe opaque any more.

 

[PeterDonis]

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