As the title says, my question is how do we know how old the universe is? Thanks
Start here: http://en.wikipedia.org/wiki/Age_of_the_universe
So measurements of the cosmic background radiation give the cooling time of the universe since the Big Bang, and measurements of the expansion rate of the universe can be used to calculate it's approximate age by extrapolating backwards in time gives us the estimate of thirteen billion years as the age of the universe. Where does the cosmic background radiation come from? Thanks
Google "surface of last scattering"
As you extrapolate the expansion backwards, at some point the matter in the universe becomes so hot and dense that it turns into plasma(i.e., the electrons get stripped off atoms). Plasma is not transparent to light. Which means that before that point in time, light couldn't travel freely through the universe, bouncing off the free nuclei instead. This constant bouncing meant that all the matter was roughly at the same temperature, as the radiation would quickly transfer heat from the hotter parts to the colder. This in turn meant that the light looked as if it was emitted by a body of a certain temperature(look up blackbody radiation). That is, it had a certain range of well defined spectra.
So as the expansion passed that moment, i.e., the universe cooled enough for the nuclei to combine with electrons to form atoms, all the light that could not travel freely earlier could now escape. CMBR is that light. It's spectrum looks like that of a body at a temperature of some 3000 kelvin(which is when the plasma became transparent), stretched 1090 times. Hence you can hear of CMBR as being at 2.7 kelvin.
Since every bit of the universe was filled with plasma back then, and the expansion made all the plasma transparent at roughly the same moment, the radiation comes from all directions.
That transition from opaqueness to transparency occured some 380 thousand years after the expansion started, and the "boundary" that CMBR creates in the sky is called "the surface of last scattering".
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