# Why is there no continuity on the temperature of the CMB?

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1. Jan 4, 2016

### sandrogiongo

On the epoch of last scattering, the universe became transparent and the typical CMB photon was "free" to travel the universe. The corresponding radiation was of a black body temperature of ~3000K.

My question is: after the last scattering, the universe was still hot and, I presume, emitting radiation. Why, for example, we don't see a CMB corresponding to the epoch when the universe had 2000K, or 1500K?

2. Jan 4, 2016

### marcus

The watts per unit area goes as the fourth power of the temperature.

The spectrum for 1500 K would have the same shape and spread and placement as the spectrum for 3000 K.
So we could not distinguish. It would blend right in. A small contribution because only 1/64 as much power.

The reason is if main CMB is from z+1 = 1090, then radiation from 1500 K is from z +1 = 545, when distances were twice what they were at z+1 = 1090.
But radiation wavelengths would be TWICE. And on the way to us they would be stretched HALF AS MUCH
so the effects CANCEL. So the power spectrum curve that we would observe is just a smaller version of the
main one. It blends right in. AFAICS

See what some other people say. That is what I think.

Last edited: Jan 4, 2016
3. Jan 4, 2016

### Staff: Mentor

For a perfect blackbody. Hydrogen is not a blackbody, which makes the temperature-dependence even stronger.
Hydrogen in its ground state needs a 10 eV photon to get excited and 13.6 eV for a reasonable cross-section. The Boltzmann factor $e^{-E/(kT)}$ for this is 10-17 and 10-23 for 3000 K, respectively. Small, but there were so many photons per hydrogen atom that it was still relevant. Lower the temperature to 2700 K and the factors drop by a factor of ~100 to 1000.

There was a transition period, but it was quite short (I think something like 20000 years) in a narrow temperature range.

4. Jan 4, 2016

### sandrogiongo

Ok, then it's a matter of the power of the radiation? If so, there is a radiation corresponding to lower temperatures than 3000K which is too "weak" for us to see?

5. Jan 4, 2016

### Staff: Mentor

There is radiation emitted at a time where the universe was colder. This radiation appears hotter than the rest: it had something like 10 eV at that time (where the CMB was below 1/4 eV), so it has at least ~10 meV today, which is significantly above the energy of the CMB spectrum. It is completely negligible, however.

6. Jan 4, 2016

### Chronos

We don't notice blackbody radiation from when the CMB source was less than 3000K because it's like trying to discern a candle flame in front of a spotlight, as marcus noted. Not that it isn't there, it's merely washed out by the radiation already unleashed.

7. Jan 5, 2016

### sandrogiongo

Ok, guys! Thank you!