Cosmological Redshift: Why Does k Remain the Same?

[karlzr]

condidering a photon in expanding cosmos, it 's said that the wavenumber k remains unchanged, the wavelength \lambda increases, proportional to the scale factor a(t) of the universe, and the frequency w decreases in the opposite way, that is the cosmic redshift.

so, why does k remain the same?

 

[bcrowell]

Hi, karlzr -- By the way, to make Greek letters show up, you have to surround them in itex tags. To see how to do that, click on the Quote button for this post, and look at how I did this one: $\lambda$.

I don't think it's true that k stays the same. The four-vector $(f,k)$ is a lightlike vector for a light wave, so f=k (in units where c=1). Since f experiences a cosmological red-shift, k must go down as well. Also, as far as I know k is simply defined as $1/\lambda$, so $1/\lambda$ can't vary independently of k.

Conceivably the answer could be different if you weren't talking about propagation in vacuum, since the k and f are related by the phase velocity, which doesn't have to equal c. So then I could imagine that it would be possible to have f and k not related in the usual way, although I think you'd still have $k=1/\lambda$ as a matter of definition.