Jacek

So 3000K was a temperature of hydrogen at that time?

In my understanding, the background radiation was already there before the recombination, when the hydrogen atoms were created, and some of it was absorbed by them in the process of their creation. However, the electrons in newly formed atoms were generally in the excited state from which they immediately transitioned to the ground state, emitting the photons that were added back to the background radiation. Is this correct? If it is, then the idea of extrapolating it back to the Big Bang seems sensible to me the more if the radiation coexisting with the plasma before the recombination was the black body radiation. If it's not, then I'm left with the purely mathematical extrapolation, but I don't see how it could be incorrect, since the radiation's redshift directly corresponds to the scale factor describing the equal expansion of the universe and the radiation filling it. What I can show is trivial. "According to the FLRW metric which is used to model the expanding universe, if at present time we receive light from a distant object with a redshift of z, then the scale factor at the time the object originally emitted that light is a(t)=1/(z+1)." [imath]1+z=1/a(t)[/imath] I'm aware that [imath]dz/dt = -\dot{a}/a^2 = -(1/a)(\dot{a}/a)[/imath] [imath]\dot{a}/a = H(t) = H(z(t)) = H(z)[/imath] [imath]dt = -(1+z)^{-1}H(z)^{-1}dz[/imath] But I'm not using it; dz is the differential of dimentionless redshift, and I need dimentional, temporal dt and spatial cdt. It's enough for me that 1/a(t)=1+z(t), so dt/a(t)=(1+z(t))dt. Now, if we interpret dt as the initial period and cdt as the initial wavelength at - let's say - the Planck time, then z(t)+1 is the redshift+1 equal to the expansion of the wavelength, period and the universe itself. Ps. What's the deal with latex?

I can't show it in "my" integral, because it's not mine. It's the integral of the FLRW metric equation for null geodesic. I'm just giving you my interpretation of cdt/a(t) as the extending wavelength, and dt/a(t) as the extending period over time counted backwards. Ps. I've reached the maximum number of posts I can make per day. That's a limitation for a new accounts on this forum. @swansont I will gladly answer you tomorrow.

But I see it. If you extrapolate the CMB peak wavelength backwards to the Big Bang, then it will be infinitesimally short, just like the differential dt. That's why I consider cdt/a(t) as the extending wavelength, and dt/a(t) as the extending period, but with time counted backwards.

I don't choose a single one. I'm adding their changing periods just like I'm adding a changing wavelengths by integrating over cdt/a(t) to get the observable universe radius. Conformal age 47Gy is conformal, because it's proportional to the observable universe radius equal to 47Gly, and the proportionality factor is the speed of light. In the same way the extending radiation periods are all proportional to the extending wavelengths. That makes them conformal.

Which one are you? :)

SI definition of a second: "The duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom." If we give the cosmic time (equal to the universe age equal to the proper time of the observer resting in the CMB reference frame) in seconds, we can easily give it in the number of radiation periods from SI definition of a second. In the same manner we can define a physical, conformal age of the universe. That's the duration of a certain number of the extending CMB radiation periods proportional to the extending peak wavelength of this radiation that passed through a point at which the CMB is isotropic, since its emission. Proportionality factor is the speed of light, because c=λ/T where λ is the extending peak wavelength, and T is the extending wave period. Conformal time η=∫dη=∫dt/a(t)=47Gy is the conformal age of the universe and I don't question it. I'm proposing a physical definition for it. The inverse of the scale factor 1/a(t) is increasing with time counted backwards, because 0<a(t)≤1 and a(t₀)=1, where t₀ is the present, proper age of the universe. That makes dt/a(t) the equivalent of the wave period extending over time counted backwards. We're integrating over it to sum it up. Is there something wrong with the proposed, physical definition?