Rick's Cosmology Tutorial: Chapter 4 Abstract

The Measured Microwave Background Temperature

Following on from Chapter 3 we derive the temperature of the cosmic background photons in the matter dominated era. The predicted cosmic microwave background (CMB)temperature is 3.8 K. This compares with extremely accurate measurements (COBE/WMAP) which give 2.728 K. The agreement is impressive given the simplicity of our derivation. The existence of the CMB with the correct temperature is one of the key successes of the Big Bang theory. Historically it was the discovery of the CMB which killed off the rival steady state theory in the 1960s. The measured temperature of the CMB is used to refine our estimate of the temperature-time relations for use in subsequent Chapters. The CMB temperature provides the photon number density through the black body formula. Together with an estimate of the mean density of ordinary matter this allows the photon:baryon ratio to be estimated as 1.9 x 10^9.

Uses: Both the revised temperature-time relations and the photon:baryon ratio are crucial in the evolution of the universe, as will be seen in subsequent Chapters.

Warning: The prescription given for temperatures in the matter dominated era apply only to the photons (i.e. the CMB )and, suitably adjusted, to the neutrinos. It does not apply to the matter content of the universe. Initially this is because matter and electromagnetic radiation stop interacting at roughly the same time that matter becomes dominant (see Chapters 8,9,10). Hence, they are no longer held in thermal equilibrium. Later on, gravitational clumping of some of the matter takes place. This has a dramatic effect on the temperature of the matter involved. It also causes the matter densities and temperature to become highly inhomogeneous.

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Cat's Eye Nebula (NGC6543), discovered by William Herschell, 1786. It is a planetary nebula in the constellation of Draco. In the center of the Cat's Eye there is a bright, hot star, which ejected its outer envelop about 1000 years ago, producing the nebula.