Caption: The nearly perfect blackbody spectrum (plot in the frequency representation (x_max = hν/(kT) = 2.821439372122078893... , F(x_max) ≅ 0.365)) of the cosmic microwave background (CMB) from the Cosmic Background Explorer (COBE, 1989--1993).

Currently, the best result for CMB Temperature T = 2.72548(57) K (Fixsen 2009).

Features:

1. The continuous curve is a fitted blackbody spectrum. The actual error bars are too small to be seen. Crosses are put just to show where the data points are.

2. The plot is of specific intensity (in the frequency representation (x_max = hν/(kT) = 2.821439372122078893... , F(x_max) ≅ 0.365)) versus wavenumber (with units cm**(-1)). Note, frequency representation means ∼ 36.5% of the energy is blueward of the maximum and ∼ 63.5 % of the energy is redward of the maximum.

   Wavenumber is inverse wavelength measured in this case in inverse centimeters. It is also frequency divided by the vacuum light speed 2.99792458*10**10 cm/s, and so it is actually a frequency. Wavenumber is given by the formula

         ν_wavenumber = 1/λ = f/c .

3. The microwave band (fiducial range 0.1--100 cm) corresponds to wavenumber range 0.01--10 cm**(-1). So the CMB is centered in the microwave band though it extends significantly to larger wavenumber (i.e., shorter wavelength) than the fiducial range of the microwave band (as the plot shows) and probably a bit to smaller wavenumber (i.e., larger wavelength) than the fiducial range of the microwave band.
   Why microwaves are called microwaves when they are of order centimeters in wavelength is beyond yours truly. They should be called CENTIWAVES. But no one ever listens to yours truly.

4. The CMB is one of the most perfect blackbody spectra to be found in nature. Thus, it corresponds to nearly a single temperature.

5. Currently, the best result for CMB Temperature T = 2.72548(57) K (Fixsen 2009) (see also Wikipedia: Cosmic microwave background radiation: Features).

6. Wien's law for wavenumber (with units cm**(-1)) and intensity (energy/(area*steradian*time*1/length)) is

         ν_{wavenumber maximum} = (1.96099855 K/cm) * T ,

   which for T=2.72548 K gives

         ν_{wavenumber maximum} = (1.96099855 K/cm)*(2.72548 K) = 5.34466 cm**(-1) .

   As far as yours truly can read the plot, the maximum is at ∼ 5.3 cm**(-1), and so the calculation agrees with the plot as far as yours truly can tell.

7. The CMB is one of the strongest evidences for Big Bang cosmology:
   1. Big Bang cosmology includes the proposition that the early expanding universe had a hot phase where ionized matter (by mass fraction ∼ 75% hydrogen and 25 % helium) was in thermodynamic equilibrium with electromagnetic radiation (EMR) at a single temperature. This EMR field was, of course, a blackbody radiation field and is still called the cosmic microwave background (CMB) by convention even though only much later in cosmic time did it mostly in the microwave band (fiducial range 0.1--100 cm).

   2. The expanding universe cooled both matter and the CMB (still in mutual thermodynamic equilibrium) through adiabatic expansion, and at some point reached the temperature and density conditions where helium and then hydrogen recombined with free electrons to form neutral atoms. This event is called the recombination era t = 377,770(3200) Jyr = 1.192*10**13 s (z = 1089.80(21)).

   3. The loss of free electrons rapidly changed the expanding universe from being largely opaque to being nearly transparent to the CMB.

   4. The CMB at the recombination era t = 377,770(3200) Jyr = 1.192*10**13 s (z = 1089.80(21)) had a temperature of order 3000 K.

   5. After the recombination era the CMB evolved as an expanding photon gas in the expanding universe that only negligibly interacted with matter. Occasionally, a photon will scatter off an free electron or be absorbed by a star, planet, or one of our dectors, but most of the photons just stream freely through space NEVER hitting anything ever.

   6. Expansion adiabatic cooled the CMB while maintaining it as a blackbody radiation field even though it was NOT interacting with matter. It is a remarkable feature of adiabatic cooling that a blackbody radiation field stays a blackbody radiation field while cooled. The current CMB temperature is 2.72548(57) K (see Wikipedia: Cosmic microwave background radiation: Features) which makes the CMB significant only in and near the microwave band (fiducial range 0.1--100 cm, 0.01--10 cm**(-1)). Hence, we call the current CMB the cosmic microwave background (CMB).

   7. Despite a lot of ingenuity, no one has thought any natural (i.e., non-ad-hoc) way of creating the CMB in an expanding universe other than in Big Bang cosmology.

      Thus, the CMB as aforesaid is strong evidence for Big Bang cosmology.

      The complete evidence for Big Bang cosmology is quite convincing.

      It would be astonishing if it were just plain wrong.

8. Note, the cosmic microwave background (CMB) spectrum was subject to some small overall cosmic microwave background spectral distortions at high cosmological redshift z (see Wikipedia: Cosmic microwave background spectral distortions). This is a finicky topic we will NOT go into. The cosmic microwave background spectral distortions are NOT to be confused with the distinct cosmic microwave background (CMB) temperature fluctuations (see Cosmology file: cmb_power_spectrum.html).