The cosmic background radiation

Following the idea that the universe was very hot and dense, George Gamow suggested, in 1946, that when the universe was less than about 200 seconds old, the temperature was greater than one billion kelvin, hot enough for nuclear reactions to take place rapidly. In 1948, Ralph Alpher, Hans Bethe and Gamow showed (in a paper often referred to as the alpha/beta/gamma (for the names of the authors) paper) that these nuclear reactions might be able to explain the current abundance of helium in the universe. (We will discuss the synthesis of the elements in the next section.) In a more thorough analysis of the problem, Alpher and Robert Herman, in a classic paper published in 1948, found that the early universe should have been filled with radiation, and that the remnant of that radiation should still be detectable as a low intensity background of microwaves.

21.1.1 Origin of the cosmic background radiation

To help visualize the evolution of the early universe, we again rely on an analogy with an expanding sphere, as shown in Fig. 21.1. Remember, in this analogy, the universe is the surface of the expanding sphere. All particles and radiation must move along the surface. If you have a balloon, you can follow along with this analogy.

When the universe was young enough to have its temperature higher than 3000 K, the atoms were all ionized. The universe was a plasma of nuclei and electrons. The free electrons are particularly efficient at scattering radiation. They provided a continuum opacity for any radiation present. This means that radiation would not travel very far before getting scattered; the universe was opaque. The radiation therefore stayed in equilibrium with the matter. The spectrum of the radiation was that of a blackbody at the temperature of the matter. As the universe expanded, the density decreased, and the temperature decreased. As the matter cooled, the radiation also cooled. Then the point was reached at which the temperature dropped below 3000 K. (Various estimates place this at a time some 100 000 years after the expansion started.) At the lower temperature, the electrons and nuclei (mostly protons, or helium) combined to make atoms. This is called the era of recombination. The neutral atoms are very inefficient at absorbing radiation, except at a few narrow ranges of wavelengths corresponding to

spectral lines. For all practical purposes, the universe became transparent to the radiation. Since the radiation and matter no longer interacted significantly, we say that they were decoupled.

If we look at Fig. 21.1, we see that the last photons emitted by the plasma just before decoupling should still be running around the universe. A relatively small fraction of those photons have bumped into galaxies, and have been absorbed by

Diagram showing radiation and matter in an expanding universe. (Remember, this is a two-dimensional analogy.) (a) Before decoupling.The matter is dense and hot and the matter and radiation are in equilibrium. (b) At decoupling the universe is transparent, and the radiation now moves around without being absorbed. Photons are moving in all directions. (c) Protogalaxies are starting to form. Photons are moving in all directions and are redshifted as the universe expands. (d) Galaxies have formed, and photons are still moving in all directions.The redshift becomes larger as the universe expands. (e) Today, an inhabitant of any galaxy would see the redshifted photons coming at them from any direction.

the material in the galaxies. Anyone in one of those galaxies, looking around, should see radiation coming at them from all directions. The radiation does undergo one change. As the universe expands, all of the radiation is redshifted, a result of the cos-mological redshift. This is illustrated in Figs. 21.1(d) and (e).

We can calculate what this redshifted black-body radiation will look like. To do this, we note that the photons will be preserved; their frequencies will just change in a known way. For a black-body at a temperature T, the energy density in photons with frequencies between v and v + dv is given by the Planck function,


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