In article ,
wrote:

Here's the reason the neutrino background should be colder.
In the very early Universe, there should have been thermal
distributions of photons, electrons, positrons, and neutrinos,
all at the same temperature. When the temperature dropped
below a certain value (roughly kT = rest energy of an electron),
the electrons and positrons almost all annihilated, leaving
behind only the relatively few electrons we see around us today.

When that happened, the energy that had been in the form of electrons
and positrons got transferred to the photons, so the photons
got to be a bit hotter than the neutrinos.

Huh. Something I read made me say the neutrinos were
colder than the photons because the photons were reheated
by *nucleosynthesis* about 3 minutes after the Big Bang.
Seems to me that both effects would occur. But maybe the
electron-positon annihilation was a lot more important?

Side-remark 1: Wouldn't recombination heat up the cosmic
microwave background radiation, too?

Side-remark 2: Primordial nucleosynthesis would have made
a bunch of new neutrinos, too. A lot fewer than the original
ones, but more energetic, no? Or maybe not?? I could figure
this out if I had more time....

In article , John Baez
wrote:

In article ,
wrote:

When that happened, the energy that had been in the form of electrons
and positrons got transferred to the photons, so the photons
got to be a bit hotter than the neutrinos.

Huh. Something I read made me say the neutrinos were
colder than the photons because the photons were reheated
by *nucleosynthesis* about 3 minutes after the Big Bang.
Seems to me that both effects would occur. But maybe the
electron-positon annihilation was a lot more important?

Exactly.

The key number to remember here is that factor of a billion: there are
a billion CMB photons for every X in the Universe today, where X is
one of {electron,proton,nucleus}.

It's true that new photons must have been produced during
nucleosynthesis, but assuming that the number of new photons produced
was of order 1 (or in any case of order much less than a billion) per
nucleus, that'll have a tiny effect on the CMB temperature.

The reheating during the electron-positron annihilation epoch is
different: before electron-positron annihilation, there was of order
one electron per photon, so they cause significant photon heating when
they annihilate. It's only after annihilation that that factor of a
billion applies.

[Followup question: what about the epoch of proton-antiproton
annihilation? Doesn't that heat up the photons by a similar amount?
Answer: Yes, it does. But unlike electron-positron annihilation,
proton-antiproton annihilation didn't induce a temperature difference
between photons and neutrinos, because it happened at an earlier
epoch, when photons and neutrinos were still in thermal equilibrium
with each other. Both photons and neutrinos wound up being heated
when the protons and antiprotons annihilated.]


Side-remark 1: Wouldn't recombination heat up the cosmic
microwave background radiation, too?

The same sort of thing applies here. During recombination, about one
new photon was created per hydrogen atom, but that produces only about
a 1 part per billion change in the CMB temperature, because there's
only one hydrogen atom per billion photons.

This is also the answer to a related and (a little bit) common
question about the microwave background. People ask why we don't see
spectral lines in the CMB due to recombination. After all, those
photons produced during recombination aren't continuum photons; they
(many of them, anyway) are hydrogen spectral lines. Why don't we see,
say, the H-alpha line redshifted by a factor of 1000 when we look at
the microwave background? The answer is that that line has a strength
of order one part per billion, so it's impossible to see.

[Not just hard, but actually impossible, I think: it's way below the
intrinsic photon noise of a 3 K blackbody.]

Side-remark 2: Primordial nucleosynthesis would have made
a bunch of new neutrinos, too. A lot fewer than the original
ones, but more energetic, no? Or maybe not?? I could figure
this out if I had more time....

Yes. Again, of order one per nucleus, so the number is tiny. I don't
know about "a lot more energetic," though. I think all the energies
should be the same in order of magnitude. After all, the reason
nucleosynthesis happened when it did is that that was the time when
the temperature was of the same order of magnitude as that of nuclear
reactions. Right?

-Ted

--
[E-mail me at , as opposed to .]

wrote in message ...
[Followup question: what about the epoch of proton-antiproton
annihilation? Doesn't that heat up the photons by a similar amount?
Answer: Yes, it does. But unlike electron-positron annihilation,
proton-antiproton annihilation didn't induce a temperature difference
between photons and neutrinos, because it happened at an earlier
epoch, when photons and neutrinos were still in thermal equilibrium
with each other. Both photons and neutrinos wound up being heated
when the protons and antiprotons annihilated.]


Follow up again:-) what about the epoch of neutron-antineutron
annihilation? Would that heat up photons?

Is there an epoch where measons annihilate themselves?

Are there antineutrinos in the model?

In article ,
John Devers wrote:

Follow up again:-) what about the epoch of neutron-antineutron
annihilation? Would that heat up photons?

I guess that must happen at pretty much the same time as proton-antiproton
annihilation. It'll heat up the photon background in the same
way, and since neutrinos are still thermally coupled to photons
(via electrons and positrons) at that time, it'll also heat up
the cosmic neutrino background.

Is there an epoch where measons annihilate themselves?

Yes. Each species of massive particle annihilates roughly when the
temperature T of the Universe is given by kT = mc^2, where m is the
mass of the particle. So light mesons annihilate a bit after protons
and neutrons, but long before electrons.

Are there antineutrinos in the model?

Yes. The cosmic neutrino background should consist of equal numbers
of neutrinos and antineutrinos.

-Ted

--
[E-mail me at , as opposed to .]

"I think the burden is on those people who think he didn't have weapons
of mass destruction to tell the world where they are." --Ari Fleischer