# Have CMB photons “cooled” or been “stretched”?

Introductory texts and popular accounts of why we see the "once hot" CMB as microwaves nearly always say something about the photons "cooling" since the Big Bang. But isn't that misleading? Don't those photons have long ("cool") wavelengths because space expanded since they were emitted. There's no separate "cooling" process, is there?

-
Maybe they have been ironed flat? –  Georg Apr 16 '11 at 16:51

Cooling and stretching essentially mean the same thing here. The temperature of any blackbody radiation is related to the peak wavelength by Wien's Law $$\lambda_{\mathrm{max}} = \frac{b}{T}$$ Therefore as the universe expands, all of the photon wavelengths get stretched out and so does the peak wavelength. $$\lambda \propto a(t)$$ This decreases the temperature of the radiation by the same factor that expands the wavelength of the photons. $$T \propto \frac{1}{a(t)}$$ This factor $a(t)$ is the scale factor of the universe and increases with time for an expanding universe.

-