Cosmic Microwave Background Radiation

Light currently reaching us from the most distant known quasar (as of March 10, 2005), as may be determined from redshift measurements, was emitted at a time when the scale factor was a = 1/(1 + z) = 0.135. From these statements, one may conclude that the light we see from the quasar was emitted when the age of the universe was only te = 0.06 H0-1 = 800 Myr, which is about 6% of the current age of the universe. Fascinatingly, it was realized fairly recently that it is possible to look still further back into the history of the universe. The oldest photons are those belonging to the cosmic microwave background, discovered by Penzias and Wilson in 1964; collectively these photons form a snapshot of the universe at about 300,000 years, long before galaxies formed.

About 100,000 years after the Big Bang, the temperature of the universe had dropped sufficiently for electrons and protons to combine into hydrogen atoms, p + e~^>H + y (6.2)

The symbol y throughout this chapter denotes a gamma ray, or high-energy photon. At this time, the universe became transparent, because the photons of the cosmic microwave background radiation could no longer scatter with free electrons. This is therefore called the time of last scattering.

Following the time of last scattering, radiation was effectively unable to interact with the background gas; the radiation has propagated freely ever since, while constantly losing energy because its wavelength is stretched by the expansion of the universe. Originally, the radiation temperature was about 3000 Kelvin, whereas today it has fallen to less than 3 Kelvin! The Cosmic Background Explorer (COBE) satellite, launched in 1989, measured the spectrum of the cosmic microwave background over the entire sky for a wide range of wavelengths, and thus ushered in the current "golden age" of observational and theoretical cosmology.

At any point on the sky, the spectrum of the CMB is remarkably close to an ideal blackbody spectrum, as shown in Figure 6.4.

Frequency (cm-1)

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Figure 6.4 Intensity versus frequency for the cosmic microwave background, shown together with an ideal blackbody curve at temperature 2.7277 K.

This blackbody spectrum, it is widely believed, could only have come from a universe that was hot and opaque in its early stages. The expansion of the universe has the effect that the radiation cools while its thermal spectrum remains a blackbody. You can judge for yourself how closely the match of the CMB power spectrum is to a blackbody, but note that the error bars in Figure 6.4 have been increased by 400 times to make them visible!

Small temperature fluctuations in the CMB result from small density fluctuations at the time of last scattering. In more detail, a photon that happens to be in a more dense region when the universe becomes transparent will lose energy as it climbs out of the potential well generated by the excess density. It is widely believed that the low-amplitude density fluctuations that, if present at the time of last scattering, would give rise to the CMB spectrum we observe today, and they arose from quantum mechanical fluctuations in the very early universe, which were subsequently amplified through a mechanism known as inflation. Inflation was proposed by Alan Guth, and it holds that there was a period in the early universe during which the expansion function a (t) (mentioned previously) takes the form

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