By definition z = λobs / λemit -1 an so this relatiion Is always valid, even for CMB redshift or any other reshift. If you apply this definition to cosmology you find a natural relation between z and a(t): 1+z = a0/a(t) as it was stated by Dario Bettoni. You can compute z by knowing the current temperature of CMB (2.73K) and the temperature needed for recombination (neutralization of hidrogen and helium atoms) whis is aproximately 3000K. This was the "last" time photons were dispersed by electrons an protonsa the the media became transparent for CMB. In cosmoloygy it is found that Tobs=Temmited/(1+z)=Temmited(a(t)). So if Temitted=3000 and Tobs=2.7 z~1100. In the case of any question just ask.
The redshift relation can be equivalently written as 1+z = a0/a(t) where a is the scale factor of the Friedamnn-Robertson-Walker metric given by the line element ds^2=-dt^2+a^2dx^2 where a is a function of time. Assuming the energy content of the universe since CMB is dominated by dust then we have a(t) =a0(t/t0)^(2/3), where a0 and t0 are present values for the scale factor and the cosmic time respectively. Now roughly speaking t0 is of the order of 10^9 while t_CMB is aorund 10^5. then (10^9/10^5)^(2/3) = 10^(8/3) roughly 10^3, in good agreement with serious calculations. If you need more on this give a look to any cosmology textbook. You will find the full detailed calculations.
By definition z = λobs / λemit -1 an so this relatiion Is always valid, even for CMB redshift or any other reshift. If you apply this definition to cosmology you find a natural relation between z and a(t): 1+z = a0/a(t) as it was stated by Dario Bettoni. You can compute z by knowing the current temperature of CMB (2.73K) and the temperature needed for recombination (neutralization of hidrogen and helium atoms) whis is aproximately 3000K. This was the "last" time photons were dispersed by electrons an protonsa the the media became transparent for CMB. In cosmoloygy it is found that Tobs=Temmited/(1+z)=Temmited(a(t)). So if Temitted=3000 and Tobs=2.7 z~1100. In the case of any question just ask.
My cosmological model can estimate distance using redshift caused by the cosmic background gravitational potential, and even derived a new Hubble constant. CMB essentially is the cosmic background gravitational field itself, its temperature is the temperature of the gravitational field.
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