The CMB Temperature 177To their consternation and annoyance they found a constant low level of back-
ground noise in every direction. This radiation did not seem to originate from distant
galaxies, because in that case they would have seen an intensity peak in the direction
of the nearby M31 galaxy in Andromeda. It could also not have originated in Earth’s
atmosphere, because such an effect would have varied with the altitude above the
horizon as a function of the thickness of the atmosphere.
Thus Penzias and Wilson suspected technical problems with the antenna (in which
a couple of pigeons turned out to be roosting) or with the electronics. All searches
failing, they finally concluded, correctly, that the Universe was uniformly filled with
an ‘excess’ radiation corresponding to a blackbody temperature of 3.5K, and that this
radiation was isotropic and unpolarized within their measurement precision.
At Princeton University, a group of physicists led byRobert Dicke(1916–1997) had
at that time independently arrived at the conclusion of Gamow and collaborators, and
they were preparing to measure the CMB radiation when they heard of the remark-
able 3.5K ‘excess’ radiation. The results of Penzias and Wilson’s measurements were
immediately understood and they were subsequently published (in 1965) jointly with
an article by Dicke and collaborators which explained the cosmological implications.
The full story is told by Peebles [1], who was a student of Dicke at that time. Penzias
and Wilson (but not Gamow or Dicke) were subsequently awarded the Nobel prize in
1978 for this discovery.
This evidence for the 15-Gyr-old echo of the Big Bang counts as the most important
discovery in cosmology since Hubble’s law. In contrast to all radiation from astro-
nomical bodies, which is generally hotter, and which has been emitted much later,
the CMB has existed since the era of radiation domination. It is hard to understand
how the CMB could have arisen without the cosmic material having once been highly
compressed and exceedingly hot. There is no known mechanism at any time after
decoupling that could have produced a blackbody spectrum in the microwave range,
because the Universe is transparent to radio waves.
Spectrum. In principle, one intensity measurement at an arbitrary wavelength of
the blackbody spectrum (6.10) is sufficient to determine its temperature,푇, because
this is the only free parameter. On the other hand, one needs measurements at differ-
ent wavelengths to establish that the spectrum is indeed blackbody.
It is easy to see that a spectrum which was blackbody at time푡with temperature푇
will still be blackbody at time푡′when the temperature has scaled to
푇′=푇
푎(푡)
푎(푡′)
. (8.5)
This is so because, in the absence of creation or annihilation processes, the number of
photons,푛훾푎^3 (푡), is conserved. Thus the number density d푛훾(휈)in the frequency interval
(휈,휈+d휈)at time푡transforms into the number density at time푡′,
d푛′훾(휈′)=[
푎(푡)
푎(푡′)
] 3
d푛훾(휈). (8.6)