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Relicta

Cosmic Microwave Background / Relic Blackbody Physics

\[T(z) = T_0\,(1+z)\]
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Relicta is a Pixelated Physics law character, one of our relativity and cosmos designs. The cosmic microwave background was released when the universe was about 3000 K; expansion has since stretched it to 2.7 K. This is a 3" × 3" pixel-art sticker. The physics panel below gives the equation, what each symbol means and the sources.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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The physics

The cosmic microwave background is light left over from when the universe became transparent. It has a nearly perfect blackbody spectrum, and its temperature has fallen in proportion to the stretching of space, to about 2.7 K today.

Relicta is a retired fire. She once glowed at about 3000 K; now she sits at 2.7 K, and she is still a perfect blackbody.

For its first few hundred thousand years the universe was a hot plasma, and light could not travel far before scattering off free electrons. As it cooled to about 3000 K, electrons and nuclei joined into neutral atoms and the universe turned transparent. That moment, decoupling or last scattering, came at a redshift z of about 1090 (Planck 2018: 1089.92). The light released then has been travelling ever since.

As space expanded, the wavelengths of that light stretched with it by a factor of 1 + z, so its temperature fell in the same proportion, the first line on this page. Photons stretch; atoms, galaxies and Relicta do not. Stretching a blackbody gives a cooler blackbody, so the shape of Planck’s curve, the third line, has never changed. Today it peaks at about 160 GHz, in the microwaves. On a wavelength axis the peak falls at 1.06 mm, a different point, not c divided by 160 GHz.

In 1965 Arno Penzias and Robert Wilson at Bell Labs found a stubborn excess hiss in their horn antenna, the same in every direction, equivalent to about 3 K. They shared in the 1978 Nobel Prize. In 1990 the first spectrum from NASA’s COBE satellite, measured by John Mather’s team, matched a blackbody almost perfectly; Mather and George Smoot shared the 2006 Nobel Prize. Dale Fixsen’s 2009 value for today’s temperature is 2.72548 K, the second line.

Her old photo and her new cardigan show the same curve with a different scale. Retirement, not decay.

I was 3000 K once. Now I’m 2.7 K.

Equations

\[T(z) = T_0\,(1+z)\]
\[T_0 = 2.72548\ \text{K}\]
\[B_\nu(T) = \frac{2h\nu^3}{c^2}\,\frac{1}{e^{h\nu/k_B T}-1}\]
\[\nu_{\text{peak}} \approx 160\ \text{GHz}\]
Symbols
SymbolMeaningUnit
\(T(z)\) temperature of the background radiation at redshift z \(\mathrm{K}\)
\(z\) redshift (last scattering: about 1090) \(\mathrm{1}\)
\(T_0\) temperature today (Fixsen 2009: 2.72548 ± 0.00057 K) \(\mathrm{K}\)
\(B_\nu\) blackbody spectral radiance per unit frequency \(\mathrm{W·m^{-2}·Hz^{-1}·sr^{-1}}\)
\(\nu\) frequency \(\mathrm{Hz}\)
\(h\) Planck constant \(\mathrm{J·s}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(\nu_{\text{peak}}\) frequency where today's spectrum peaks (on a wavelength axis the peak is at 1.06 mm, a different point) \(\mathrm{Hz}\)

Source Penzias, A. A.; Wilson, R. W. (1965). A Measurement of Excess Antenna Temperature at 4080 Mc/s. The Astrophysical Journal 142, 419.doi.org/10.1086/148307 (opens in a new tab)