# Does space expansion affect the CMB photon frequency?

I have read this question:

Effect of expansion of space on CMB

where Ted Bunn says:

For definiteness, let's consider a wave packet of electromagnetic radiation with some fairly well-defined wavelength. At some early time, it has a wavelength $$\lambda_1$$ and energy $$U_1$$. (I'm not calling it $$E$$ because I want to reserve that for the electric field.) After the Universe has expanded for a while, it has a longer wavelength $$\lambda_2$$ and a smaller energy $$U_2$$. (Fine print: wavelengths and energies are measured by a comoving observer -- that is, one who's at rest in the natural coordinates to use.) In fact, the ratios are both just the factor by which the Universe has expanded: $${\lambda_2\over\lambda_1}={U_1\over U_2}={a_2\over a_1}\equiv 1+z,$$ where $$a$$ is the "scale factor" of the Universe. $$1+z$$ is the standard notation for this ratio, where $$z$$ is the redshift.Just to be clear: by "amplitude" you mean the amplitude of a classical electromagnetic wave -- that is, the peak value of the electric field -- right? In that case, the answer is that the amplitude goes down.

But the CMB does have a certain redshift.

The cosmic microwave background has a redshift of z = 1089, corresponding to an age of approximately 379,000 years after the Big Bang and a comoving distance of more than 46 billion light years.

https://en.wikipedia.org/wiki/Redshift

Is this a contradiction? This does not explain whether the CMB's photons' wavelengths themselves are getting stretched as the universe expands.

Question:

1. Do the CMB's photons wavelength get stretched as they travel through expanding space or is the CMB redshift constant?

I don't see the contradiction. The wavelength of light stretches with time in the way that you wrote. The wavenumber $$k=2\pi/\lambda$$ decreases accordingly.