Isotropy in the cosmic background

Apart from the small fluctuations discussed above (one part in 100,000), the observed cosmic microwave background radiation exhibits a high degree of isotropy, a zeroth order fact that presents both satisfaction and difficulty for a comprehensive theory. On the one hand, it provides a strong justification for the assumption of homogeneity and isotropy that is common to most cosmological models. On the other hand, such homogeneity and isotropy are difficult to explain because of the “light-horizon” problem. In the context of the cosmic microwave background, the problem can be expressed as follows. Consider the background radiation coming to an observer from any two opposite sides of the sky. Clearly, whatever are the ultimate sources (hot plasma) of this radiation, the photons, traveling at the speed of light since their emission by the plasma, have only had time to reach Earth now. The matter on one side of the sky could not have had time to have “communicated” with the matter on the other side (they are beyond each other’s light horizon), so how is it possible (with respect to an observer in the right rest frame) that they “know” to have the same temperature to a precision approaching one part in 100,000? What accounts for the high degree of angular isotropy of the cosmic microwave background?

A mechanism called “inflation” offers an attractive way out of this dilemma. The basic idea is that at high energies, matter is better described by fields than by classical means. The contribution of a field to the energy density (and therefore the mass density) and the pressure of the vacuum state need not have been zero in the past, even if it is today. During the time of superunification (Planck era, 10⁻⁴³ second) or grand unification (GUT era, 10⁻³⁵ second), the lowest-energy state for this field may have corresponded to a “false vacuum,” with a combination of mass density and negative pressure that results gravitationally in a large repulsive force. In the context of Einstein’s theory of general relativity, the false vacuum may be thought of alternatively as contributing a cosmological constant about 10¹⁰⁰ times larger than it can possibly be today. The corresponding repulsive force causes the universe to inflate exponentially, doubling its size roughly once every 10⁻⁴³ or 10⁻³⁵ second. After at least 85 doublings, the temperature, which started out at 10³² or 10²⁸ K, would have dropped to very low values near absolute zero.

Inflation provides a mechanism for understanding the overall isotropy of the cosmic microwave background because the matter and radiation of the entire observable universe were in good thermal contact (within the cosmic event horizon) before inflation and therefore acquired the same thermodynamic characteristics. Rapid inflation carried different portions outside their individual event horizons. When inflation ended and the universe reheated and resumed normal expansion, these different portions, through the natural passage of time, reappeared on our horizon. Through the observed isotropy of the cosmic microwave background, they are inferred still to have the same temperatures.

Given the measured radiation temperature of 2.735 K, the energy density of the cosmic microwave background can be shown to be about 1,000 times smaller than the average rest-energy density of ordinary matter in the universe. Thus, the current universe is matter-dominated. If one goes back in time to redshift z, the average number densities of particles and photons were both bigger by the same factor (1 + z)³ because the universe was more compressed by this factor, and the ratio of these two numbers would have maintained its current value of about one hydrogen nucleus, or proton, for every 10⁹ photons. The wavelength of each photon, however, was shorter by the factor 1 + z in the past than it is now; therefore, the energy density of radiation increases faster by one factor of 1 + z than the rest-energy density of matter. Thus, the radiation energy density becomes comparable to the energy density of ordinary matter at a redshift of about 1,000. At redshifts larger than 10,000, radiation would have dominated even over the dark matter of the universe. Between these two values, at a redshift of about 1,090, radiation would have decoupled from matter when hydrogen recombined. It is not possible to use photons to observe redshifts larger than this, because the cosmic plasma at temperatures above 4,000 K is essentially opaque before recombination. These photons from a redshift of 1,090 form the cosmic microwave background.