# Cosmic Background Radiation and redshift vs. temperature

I get that the CMB has gone from high energy photons, to low microwave photons today. And that is probably due to the redshift from the expanding Universe. But, since CMB is a black body it is temperature dependent, i.e. it has a high peak at high temperatures, but then gradually gets less "peaky" and goes towards longer wavelengths.

So, is it the decreasing temperature of the Universe that is increasing the wavelength of the CMB radiation, or is it the expansion, and therefore redshift, or are they somewhat linked ?

• Redshift, in general, is a distance dependent quantity. It's small for objects that are close to us and large for distant ones. The distance at which the CMB was emitted (surface of last scattering) is a constant across the universe, which means that all observers are seeing the same redshift, which is a function of cosmological time. – CuriousOne Dec 28 '14 at 17:21

So, is it the decreasing temperature of the Universe that is increasing the wavelength of the CMB radiation, or is it the expansion, and therefore redshift, or are they somewhat linked ?

The black body radiation can be calibrated to a temperature. This is the shape of CMB, one of the best black body radiation curves:

Graph of cosmic microwave background spectrum measured by the FIRAS instrument on the COBE, the most precisely measured black body spectrum in nature. The error bars are too small to be seen even in an enlarged image, and it is impossible to distinguish the observed data from the theoretical curve

In the Big Bang model for the formation of the universe, Inflationary Cosmology predicts that after about 10^−37 seconds the nascent universe underwent exponential growth that smoothed out nearly all inhomogeneities. The remaining inhomogeneities were caused by quantum fluctuations in the inflaton field that caused the inflation event. After 10^−6 seconds, the early universe was made up of a hot, interacting plasma of photons, electrons, and baryons. As the universe expanded, adiabatic cooling caused the energy density of the plasma to decrease until it became favorable for electrons to combine with protons, forming hydrogen atoms. This recombination event happened when the temperature was around 3000 K or when the universe was approximately 379,000 years old. At this point, the photons no longer interacted with the now electrically neutral atoms and began to travel freely through space, resulting in the decoupling of matter and radiation.

The black body curve fitted to the CMB gives a temperature which is

now down to 2.7260±0.0013 K, it will continue to drop as the universe expands. The intensity of the radiation also corresponds to black-body radiation at 2.726 K because red-shifted black-body radiation is just like black-body radiation at a lower temperature. According to the Big Bang model, the radiation from the sky we measure today comes from a spherical surface called the surface of last scattering.

Italics mine.

According to the BB model the CMB is a snapshot of the black body radiation of the universe when it was 379000 years old. That is what decoupling means, that the photons on average stopped interacting/scattering because neutral atoms were formed and the crossection for interaction dropped to practically zero.

The assumption is that the observable universe is not currently radiating as a black body as its inhomogeneity no longer can be treated as a black body, in contrast until 379000 years from the beginning of the BB , when it was one homogeneous ensemble, as described above, so it cannot contaminate the spectrum within errors, which are very small.

We are not measuring the current temperature of the universe with the CMB.

If there were no expansion of space this would have retained the black body shape of ~3000K which was the temperature of the universe at that time. The fact that the CMB is so cold presently fits in the jig saw puzzle that builds up the Big Bang model consistently.

• Nice post - but I think you got your language a bit mixed up when you wrote " in contrast until 379000 years ago , when it was one homogeneous soup". I think I know what you were trying to say but would suggest that you make the edit yourself so I don't put words in your mouth... – Floris Dec 28 '14 at 18:35
• @Floris OK, soup is not very homogeneous after all. – anna v Dec 28 '14 at 19:23
• Anna, it wasn't "379000 years ago", it was billions of years ago, when the universe was only 379k years young. I wasn't really worried about the soup, but about the direction of relative measurement of time :-) – Floris Dec 28 '14 at 19:41
• @Floris you are correct of course, sorry, must be a type of dyslexia. I was not reading/writing and thinking at the same time :( – anna v Dec 29 '14 at 3:59
• Don't worry about it... my upvote finger awaits your next edit... :-) – Floris Dec 29 '14 at 4:01

Red-shifted black-body radiation is just like black-body radiation at a lower temperature, that is why you might think the two effects are mixed. The CMB comes from the time when the universe was about 379,000 years old, the time at which (as the universe expanded) adiabatic cooling caused the energy density of the plasma to decrease until it became favorable for electrons to combine with protons, forming hydrogen atoms. This recombination event happened when the temperature was around 3000 K. At this point, the photons no longer interacted with the now electrically neutral atoms and began to travel freely through space, resulting in the decoupling of matter and radiation. The the original peak of the CMB was at visible light with a temperature of about 3000K, and due to the redshift the peak is observed at at a lower wavelength of about 160.2 GHz, in the microwave range of frequencies. You can give this observed distribution a color temperature of 2.72 K (which will continue to drop due to redshift as the universe expands).

The blackbody radiation due to the cosmic microwave background was in thermodynamic equilibrium with the rest of the Universe at a temperature of about 3000K when it "decoupled".

The decoupling event (I never understand why it is often call recombination, since the protons and electrons were never combined previously), where electrons were captured by protons, made the universe very transparent to the radiation in it. Hence the blackbody spectrum was fixed at this point, at a temperature of 3000K, and would be the same today if it were not for the expansion of space.

As space expands, all wavelengths get longer by the same factor of $1+z$, where $z$ is the current observed redshift of a cosmic radiation source. The epoch at which the CMB was emitted corresponds to $z \sim 1100$, so all wavelengths have been stretched by a factor of $\sim 1101$.

Wien's law relates the wavelength the peak of the blackbody distribution to the recirocal of its characteristic temperature. Hence this peak wavelength is also shifted and so the current characteristic temperature of the CMB is $\sim 3000/1+z$, which gives the 2.7 K observed.