The matter content in the universe when the last scattering happens

[Accidently]

Assuming that the whole universe is electric charge neutral, there are neutral atoms, unbound electrons (which play the role in the last scattering), photons and decoupled neutrinos. So it seems to me there is no particle to "balance" the negative charge carried by the electrons.

Did I miss something?

 

[bapowell]

Last scattering is thought to have occurred because the free electrons and protons began to form neutral hydrogen at around z = 1100. So, it's not that you have equal number densities of neutral hydrogen and free electrons -- the electrons are used to form the hydrogen. However, I suppose it is an assumption that the densities $n_e = n_p$ at recombination, although this equality must hold at least approximately since with too many free electrons floating around, the epochs of decoupling and recombination no longer closely coincide. The assumption of $n_e = n_p$ likely stems from the idea of charge conservation in the universe -- which is a reasonable theoretical supposition and also appears to be supported observationally. While there are ionized regions of the universe, these are the result of local physics and charge is conserved in these processes; most bound structures are overwhelmingly charge neutral.

 

[Accidently]

so, if I understand correctly,
when z = 1300, the recombination happens, and a lot of electrons are captured by the protons to form hydrogen atom.
As the number of electrons declines, the Compton scattering is not likely to happen, and at z = 1100, the photons cannot scatter with electrons efficiently any more. But these electrons will keep being captured by the protons until the recombination process totally finished.

Is this correct?

But I am still wondering, if there are electrons for the last scattering, there must be protons participating the scattering with photons as well (in order to keep the universe neutral). Why they are not taken into account? Is that because the cross section is small or we just need to calculate approximately?

 

[bapowell]

I don't recall the exact redshifts of the two events, but recombination and decoupling can generally be taken to loosely coincide, with recombination occurring first. But yes, as the temperature drops neutral hydrogen begins to form and the numbers of free electrons decline. Soon the interaction rate between the photons and remaining free electrons (and between photons and the bound electrons) falls below the expansion rate of the universe and decoupling occurs.

With regards to free proton scattering, you are again correct. The Thomson scattering cross section goes like $\sim 1/m^2$ and so it is suppressed by a factor of $10^6$ relative to free electron scattering.

 

[Chalnoth]

Assuming that the whole universe is electric charge neutral, there are neutral atoms, unbound electrons (which play the role in the last scattering), photons and decoupled neutrinos. So it seems to me there is no particle to "balance" the negative charge carried by the electrons.

Did I miss something?

Positive ions, free protons balance the charge of all free electrons.

 

[Drakkith]

Sounds like another reason to have a...positive...attitude...muahahaha!

 

[Accidently]

explains everything. thanks