Is the blackbody curve of the cosmic microvave background maintained as the Universe expands? The cosmic microwave background is observed to have a blackbody spectrum. What happens to it as the Universe expands and is a blackbody curve
maintained with the expansion? I know that the spectrum will be shifting towards redder wavelengths and the peak intensity will drop (as it cools). But I cannot really figure out whether the blackbody curve will be maintained.
 A: Yes, the black body radiation follows the apparent temperature change in both shape and magnitude. 
In a hollow black body, the radiant power density per unit wavelength and per unit area given by Planck's Law
${(2hc^2/\lambda^5)/(e^{hc/{\lambda kT}}-1)}$
The shape of the curve is determined by the denominator and is the same for any $\lambda T$ product. So stretching space by some factor looks exactly the same as shrinking the temperature by the same factor.
The behavior of the total radiance or magnitude of the source comes from the numerator. The integral $d\lambda/\lambda^5$ means that the radiance goes inversely with the fourth power of the characteristic (peak) wavelength (radiant power is proportional to $T^4$). This is consistent with the idea that in an expanded universe, the photons have been diluted per unit volume but have also been diluted in energy per photon. So the radiant power has gone down by the same fourth power of the scale-factor. [note that the total photon energy is not conserved in an expanding universe.]  
So the radiation has both the correct shape and the correct magnitude corresponding to the reduced temperature. Observations of CMB match this very closely.
