Thinking about the Cosmic Background Radiation

It's a lot easier if you have a deep understanding of

• the Special Theory of Relativity and how time and space are interrelated;
• the General Theory of Relativity and curved space time.

Nevertheless, simple ideas can take us a long way.

In particular, ``local'' thinking is easy. It is the global picture that is hard. Here are some local ideas.

• Let the people (if any) on each galaxy measure time t as the time since the big bang -- according to a ``clock'' on their galaxy.
• Here and now, t is approximately 10 billion years.
• The nearby matter is (on average) moving away from us according to the Hubble law.
• For a person on another galaxy at the same time t, the situation looks the same.
  • Nearby matter is (on average) moving away from the other galaxy according to the Hubble law.
  • The Hubble constant is the same.
  • The person does not see an edge of the universe.
• At earlier times t the expansion should have been somewhat faster, because gravity would have slowed it down.
  • That is, the Hubble constant would have been bigger.
  • How much bigger depends on how much mass there is.

We had a gas of protons, electrons, and lots of photons.

Here is what you would see.

You can see just a little way because the ionized gas is opaque.

Now think about what we would see a mere 5 million years after the big bang.

We had a gas of atoms and lots of photons.

Here is what you would see.

You can see a rather long way.

• But light has a finite speed.
• So the light you see from further away came from events further in the past.
• Looking 4 light years back, the light came from the hot, opaque gas.

If we look now, we can see back in time many billions of years. That's not very local.

• We can describe distant objects by their redshift, usually denoted by z.
  1 + z = (wavelength observed)/(original wavelength)

• Then z serves as a kind of cosmic distance measure.
• Bigger z corresponds to earlier times.
• With a little relativity, one finds that z --> infinity corresponds to t --> 0.
• Looking to z ~ 1000 corresponds to t ~ 1 million years.
• That is the ``decoupling'' time when atoms formed.
• The temperature at that time was about 3000 K.
• The photon spectrum at that time was a blackbody spectrum corresponding to 3000 K.
• But the light is redshifted by a factor of 1000.
• So now we see blackbody radiation corresponding to a temperature of about 3 K.