What is the Cosmic Microwave Background? I: Primordial Blackbody

Let's start with the big picture and ask the simple question, "What is the cosmic microwave background (CMB)?". Let's imagine we have a radio/microwave telescope that operates at frequencies near 100 GHz and allows us to tune to a range of frequencies. How do we observe the CMB? Simple, point to any location on the sky! Unless you happen to be looking in the galactic plane or at a synchrotron source, then the majority of light hitting your telescope will be coming from the CMB. Once we've found the CMB, let's try changing our observed frequency a bit. If we compare the strength of the light in the range from, say, 50 to 500 GHz, we'll find that its intensity follows:

$I(\nu)=\frac{2h}{c^2}\frac{\nu^3}{e^{\frac{h\nu}{k T}}-1}$

This is a blackbody curve. We can find the temperature that the blackbody curve represents by simply measuring the location of the peak of the spectrum:

$T\sim 2\frac{\nu_p}{c}~K$

Measuring the peak, you ought to find that the temperature is around ~2.7 K. Alright, so that's the radiation field that we see, but what of it? Where did it come from? Well, we know that light is redshifted as the universe expands, following the basic law:

$\nu=\nu_0(1+z)$

where $\nu_0$ is the frequency we measure now and $\nu$ is the frequency of the same light at the time corresponding to redshift z. Thus, the light we see today would have redshifted by the above amount. Wouldn't this redshifting distort the spectrum so that it wasn't a blackbody anymore? No, it turns out if you redshift all of the light in blackbody radiation, you just get another blackbody with a lower temperature:

$T=T_0(1+z)$

This means that the effective temperature of the cosmic microwave background radiation decreases with time (or increases with redshift).

So, we now have the following two facts:

1) In all directions, we see a blackbody spectrum of temperature 2.7 K.
2) At earlier times, this radiation would have followed a blackbody spectrum represented by a higher temperature.

This implies something rather striking, that the universe itself was once a blackbody emitter! If you believe the Big Bang theory, then this was indeed the case. In fact, current theories suggest that the radiation "decoupled" at z ~ 1100. What does that mean? Well, at some point, the matter in the universe was so dense that light would not be able to travel very far without being absorbed by an atom or electron. "Decoupling" is basically the era in cosmic time in which this is no longer true.

It's not immediately obvious that such an era would be well-defined (that is, it could take a while for the photons to decouple), but it turns out that the transition is very sharp. This allows us to define what's commonly referred to as a "surface of last scattering". Don't be confused by the terminology -- the transition does not occur at a surface in space, but rather a surface in spacetime. In other words, the entire spatial volume of the universe was decoupling in a thin slice of time.

Although the term "decoupling" is common, you'll also frequently hear people talking about "recombination". Turns out this is referring to the same era in cosmic time and if you can understand the reason that the two terms refer to the same thing, you can go a long way to understanding where the CMB came from.