Why has the temperature of the cosmic background fallen since the Big Bang?

Because the universe is expanding and this causes the background temperature to decrease. The ratio of the temperature and the peak wavelength of its black body distribution is a constant,

                         k      
          Constant =   ------   T x wavelength
                        hc
which means as the expansion 'stretches' the wavelength of the light making it longer, its temperature must decrease as well.
Copyright 1997 Dr. Sten Odenwald
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