Radiation vs Matter Dominance

After a few seconds in the early Universe, the amount of matter becomes fixed and there is no longer any transformation between matter and energy and vice-versa (see also Chapter 3). The total energy density in the matter field is just related to the matter density. Since the density of the Universe is necessarily decreasing with time due to its expansion (fixed amount of mass in ever increasing volume), then the energy density of the matter is also decreasing. The energy density in the radiation field shows a different behavior with the expansion. The radiation energy density is equal to the product of the physical photon density times the average energy per photon. The energy per photon depends only on the temperature of the Universe which is cooling due to expansion. Thus, not only does the number density of photons decrease but so does their average energy.

If we consider a simple case where the radius, R, of a sphere inside the Universe is steadily increasing with time then the volume will increase as the radius cubed. Hence the number density (number of particles divided by the volume) of both the matter and the photons will go as R^-3 . However, in the case of the photons, the temperature also decreases with R and so their energy declines. This leads to the general condition that

for the the matter and radiation energy densities, respectively.

Figure 2.10 Schematic representation of the faster fall off in the energy density of radiation compared to that of matter in and expanding and cooling Universe. The point where the two energy densities are equal is indicated. This point, called recombination, is fully discussed in Chapter 3.

As graphically shown in Figure 2.10, this means that no matter what the initial state of the Universe is, the energy density in radiation (energy) decreases significantly faster with the expansion than the energy density of the matter. Therefore the Universe eventually must become matter dominated. In the case of our Universe, this takes about 100,000 years to occur. Prior to this time the Universe was radiation dominated as the energy density in the radiation field was greater than that in the matter field.

The radiation dominated era leads to an immediate problem which is discussed in more detail in Chapter 3. Recall that the ratio of photons to matter particles in our Universe is about one billion to one. When the temperature of the Universe is high, the radiation pressure is also high and this radiation pressure can physically effect matter. As matter tries to clump due to gravity, the high radiation pressure intercedes and prevents the clumping. In fact, the radiation pressure is attempting to smooth out the distribution of matter. If this was completely successful then the distribution of matter would be perfectly smooth and there would be no net gravity felt by one particle towards another (recall this was Newton's solution to the problem of the collapsing Universe). If there is no net gravity then there would be no galaxy formation (and you wouldn't have to be reading this sentence). The great challenge in understanding galaxy formation is understanding how density fluctuations can maintain their integrity and grow during the radiation dominated era of the Universe. As we will see, this may well demand the existence of dark matter.