We say that the temperature of the Cosmic Microwave Background is about $2.73\,{\rm K}$, but this temperature is measured from radiation arriving on Earth millions of years after it was emitted. So how is $T=2.73\,{\rm K}$ the "current" temperature?


The temperature of the CMB radiation being received on Earth right now is 2.73K, by which we mean it has the same spectrum of a black body with a temperature of 2.73K.

This CMB radiation was emitted 13.8 billion years ago and has been travelling in a straight line for 13.8 billion years before hitting the Earth. When the CMB radiation was emitted (about 379,000 years after the Big Bang) its temperature was about 3000K, and in the 13.8 billion years since it has been redshifted and cooled to 2.73K by the expansion of the space through which it was travelling.

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    $\begingroup$ +1, a salient point here is that, as it turns out, red- or blue-shifting a blackbody spectrum gives you another blackbody spectrum. $\endgroup$ – Al Nejati Oct 11 '18 at 8:20

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