Big Bang Age

WMAP map of the CMB. Credit: WMAP team
How long ago did the Big Bang happen? What is the Big Bang's age? 13.7 billion years, plus or minus a hundred million years or so … that's the conclusion of a team of astronomers, working primarily with the latest WMAP data.
This estimate is of the age of the Big Bang itself, and is independent of other estimates of the age of the universe, such as the age of the oldest stars, and the oldest age of radioactive matter (one of the wonderful things about all these estimates is that they are consistent!)
How can you estimate the Big Bang's age simply by observing the cosmic microwave background (CMB)? Here's how …
Start with the microwaves that seem to come, uniformly, from all directions (of course there are all kinds of things which emit microwaves – dust, stars, galaxies, even free electrons spiraling around magnetic field lines – but they all have distinctive features, so they can be subtracted). These microwaves come from the electrons which filled the universe a long time ago, just before they combined with the protons to form neutral hydrogen atoms. At the time, the ordinary matter in the universe was a gas (actually a plasma), with a temperature that was everywhere the same (it was in thermal equilibrium), and emitted black-body radiation.
Once the plasma became a neutral gas, the thermal radiation streamed free … and a tiny, tiny part of it is observed today, by exquisitely sensitive instruments such as the Wilkinson Microwave Anisotropy Project (WMAP) ones. We see it as microwaves because it has been redshifted, due to the expansion of the universe.
The CMB is the most perfect blackbody known, but it's not a perfect blackbody! It has a hot and cold pole, 180o apart, due to the motion of our solar system+galaxy. It also has fluctuations of about 1 to 10 µK (yes, that's micro-Kelvin, millionths of a degree), which look like random noise to our eyes (see above). But they're not (random); instead they are the imprints of various physical processes, mostly from the time the blackbody photons streamed free (some are due to effects of mass-energy along the path from primordial plasma to us). For example, sound; like any gas, sound could travel through the early universe's plasma, and the CMB photons retain information about the last sounds there (and then).
By carefully analyzing the fluctuations, the density of matter (and dark energy) at the time can be estimated, as well as composition of the matter (ordinary matter, neutrinos, dark matter). Plug those estimates into General Relativity equations and out pops an estimate of how fast the universe was expanding then. Compare that to an estimate of how fast the universe is expanding now (the Hubble constant), and you get an estimate of the age of the Big Bang. This WMAP page, and related ones, explains this in more detail; the main WMAP team paper on the Big Bang age is Five-Year Wilkinson Microwave Anisotropy Probe Observations: Cosmological Interpretation.
Other Universe Today articles on the Big Bang age include How Old is the Universe?, Planck Starts Collecting Light Left Over From Big Bang, and Beginning of the Universe.
And be sure to listen to the Astronomy Cast episode How Old is the Universe?.
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Inflation Theory is an extension of the Big Bang model. It was created to answer certain questions that arose from observations inconsistent with or unexplained by the Big Bang. Basically, Inflation Theory talks about a period of very rapid expansion before a relatively gradual one.
There's a continuing discussion among astronomers regarding the actual shape of
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