Summary of the lecture on 07-08-96

Primordial Nucleosynthesis

After the temperature of the Universe had dropped below a temperature of about 10⁹ Kelvin, atomic nuclei started to form. The first step was to combine protons and neutrons into deuterons. Most of the deuterons then combined with other deuterons to form He⁴. If there had been as many neutrons as protons in the early Universe, almost all nucleons would have combined into He⁴ nuclei. However, the mass of the neutron is slightly larger than that of the proton. As a consequence, the number of neutrons was always smaller than the number protons during the time when the Universe was still so hot that these particles could be spontanously created and annihilated (neutrons and protons where in thermal equilibrium). The ratio of number of neutrons to number of protons depended on the temperature (through the Bolzmann formula) and became smaller and smaller, until the neutrons and protons "froze out" (when the temperature had dropped below about 10⁹ Kelvin). Since the combination of protons and neutrons into deuterons and the subsequent combination of deuterons into He⁴ nuclei was very efficient, almost every neutron ended up in a He⁴ nucleus. The abundance of He⁴ in the Universe is therefore given by the "freeze-out" ratio of neutrons to protons. The theoretical prediction of this abundance and the observed value are in very good agreement (both about 25%).

The importance of deuterium
A very small fraction of the deuterons did not combine into He⁴ because the temperature and density had dropped to values that were too low before the reaction occured. What fraction of the deuterons survived depends very sensitively on the density of the Universe at that time. If the density was high, there were lots of collisions between the deuterons and and the fraction of surviving deuterons was small. If the density was low, a larger number of deuterons survived. It is possible to determine the density in the early Universe by measuring the deuterium abundance (deuterium is the atom that has a deuteron as its nucleus), because small differences in the density cause large differences in the deuterium abundance. It is important to understand that this only works because there is very little left-over deuterium in the first place. The density of baryonic matter (matter that consists of atoms) determined from the deuterium abundance measurements is about 3% of the critical density. From measurements of the orbital motions of galaxies in clusters of galaxies, we know that the true density of the Universe is at least 30% of the critical density. Therefore, there has to be some other type of non-baryonic matter generally referred to as dark matter.

Cosmic Microwave Background Radiation (CMBR)

After about 100,000 years the Universe had cooled to about 3000 K. At that time, the photons in the universe had so little energy that they could no longer break apart pairs of protons and neutrons that had combined into atomic hydrogen. Before, the Universe consisted mostly of charged particles. When the protons and neutrons combined it became neutral. Radiation strongly interacts with charged particles (photons are continuously absorbed and re-emitted by the charged particles). So before protons and electrons had combined, radiation and matter were strongly coupled. The Universe was opaque. Afterwards, radiation and matter were decoupled and the Universe became transparent. This is commonly referred to as the era of recombination.

If we look at the Universe in any direction at very large distances (redshift of about 1000; the most distant quasar is at a redshift of 5), we see it at the time of decoupling. The radiation originally emitted by the Universe during decoupling was that of a black body of a temperature of 3000 K and was therfore in the visible part of the spectrum (the filament in a light bulb has a temperature of about 3000 K). It is now redshifted to much larger wavelengths due to the Hubble expansion of the Universe and has the spectrum of a black body with a temperature of about 2.7 K.

One can distinguish the radiation emitted during the era of recombination from radiation coming from a star or any other objects because: 1. it is a thermal equilibrium spectrum corresponding to a temperature of 2.7 K and 2. it is isotropic - the same kind of radiations is observed in all directions.

Inflation

There are two problems in our theory of the early Universe:

The Horizon Problem (Causality Issue)
We observe exactly the same radiation in different directions in the Universe. The places from which this radiation is coming have not had a chance to "communicate" with each other by the time recombination occured since they were further apart at that time than even light could travel in the 100,000 years or so after the Big Bang (this is true for points that are separated by as little as 1 degree). For them to have exactly the same temperature, there would have to be some non-causal process that imposed this temperature on them.
Flatness Problem
If the density of the Universe is about 30% of the critical density today, it must have bee very, very close to the critical density in the early Universe. It would be very irritating not to have a theoretical explanation for this.

The theory of inflation provides explanations for both problems. When the Universe was about 10^-35 s old and had a radius of 10^-25 cm, it went through a phase of extremely rapid expansion during which it increased its size by a huge factor. Before this phase, the Universe was so small that all the different parts could communicate with each other and equalize their temperatures. This explains the horizon problem. It also explains why the Universe is so flat. The rapid expansion has "stretched out" any curvature of space that may have existed previously (similar to the inflation a baloon which makes a small area on its surface flatter).

Formation of Structure

In order to explain how the galaxies and clusters of galaxies in our Universe could form out of an early Universe that was extremely smooth (which we know from the CMBR), one needs to include dark matter which does not interact with radiation. There are two kinds of dark matter: Hot dark matter and cold dark matter. We do have some good candidates for both of them, but neither has been directly observed, yet. It seems that a combination of both hot and cold dark matter is needed to explain the large-scale structure of the Universe.

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