CMB formation

All the evidence for the Hot Big Bang tells us that the early universe was a hot, dense, plasma. Here’s a sketch of what that is like; photons are red arrows, and the regular matter (I’m not going to discuss dark matter here) appears as color-coded dots. Because hydrogen atoms could not form (they’re immediately broke up by photons), there isn’t any hydrogen yet… just protons (and other light nuclei), electrons, and photons.


Before we move on, there’s one critical piece of physics you need to know if you’re going to appreciate the full story here. Photons love to scatter off free electrons. So the photons you see in the picture above are scattering off the electrons all the time, hardly moving at all before they bump into another one. If photons can’t travel far in a straight line, then you can’t see very far… it’s like living in a fog.

As the universe grows older and expands, the photons feel the expansion and their wavelengths grow.  This is a pretty bizarre consequence of general relativity, so let’s pause for a second to appreciate that… the photon wavelengths grow as the universe expands!  The energy of a photon is E = h*nu = h*c/lambda, where h is Planck’s constant, c is the speed of light, nu is the photon frequency, and lambda is its wavelength.  As the universe expands, lambda increases, so the energy of each photon decreases.

Eventually, once the universe has expanded enough, the photons have lost enough energy that only a few are able to ionize a Hydrogen atom;  that job takes 13.6 electron volts of energy.  When the universe is about 380,000 years old (at a redshift of about z=1100), we get to a point where electrons start getting bound up in Hydrogen atoms that don’t get immediately broken up.   That starts to drastically reduce the free electron density, so the “mean free path” of photons starts getting pretty big.  The temperature of the photons is, at this point, about 3000K or so. This time period goes by several names:  “recombination” (ie the “recombining” of electrons with nuclei… though it really should be called “combination” since they were never combined in the first place!), “decoupling” (pretty soon the photons won’t scatter off electrons anymore, so they’re decoupled), and “last scattering” (because the photon mean free paths are growing so fast that soon they won’t scatter off electrons any more.)

Here’s what it looks like at that time:


Finally, as the expansion progresses, none of the photons at all have the energy required to ionize Hydrogen… so all the electrons find a nucleus (normally just a proton).  This makes the free electron density go to… zero!  Hydrogen is a clear gas, so the photons don’t have anything to scatter off at all… they just propogate in a straight line (at the speed of light, after all) through space.  Here’s what it looks like then:


We’ve reached the “neutral universe”.  No longer a plasma, it’s basically fairly-smooth (but a little bit lumpy) hydrogen gas, permeated by a sea of photons.

The expansion goes on and on (for 13 Billion or so more years);  the photon wavelengths grow and grow, which drive their temperature down and down to the 2.7K we see today.  The next picture gives a schematic version of what “today” looks like, after all that expansion.



So what does this really look like today, and what can we learn from studying those CMB photons, which haven’t scattered off anything for the past 13 Billion years?

First, let’s look at the earth (where our telescopes are), floating in space:



What does the CMB look like, if we could see every photon?


That’s right – the universe is filled with a sea of photons, going every which way.  We can only see the ones that are aimed at our telescopes though… ie those aimed at earth:


Once we’ve detected those, we can trace them backwards in time, and ask what they’re telling us about.  So let’s trace them back along their path… further and further out into space, and farther back in time (since, after all, photons travel at a finite speed):


Keep going… farther… a billion light years away, a billion years ago…


And finally, to 13 billion years ago, when they last scattered off electrons:


In this thought experiment we learn that by looking at the CMB photons we see today, we’re learning about the conditions in the universe when they last scattered off electrons, when the universe was only a few hundred thousand years old. These ancient photons, then, help us do a great deal of cosmic archeology.

So, next time you’re outside on a dark night, look up at the sky and think what you’d be seeing, if only you had microwave eyes…