Foundations of the Big Bang

Microwave Background

Expansion of the Universe

Abundance of the LIght ELements

On the basis of two observations, 1) the Universe is currently in a state of uniform expansion and 2) the Universe is filled with photons that come from background radiation at a temperature of 2.74 K, we can construct our generic cosmological model known as the Hot Big Bang model. This model is but a mere 30 years old so we should not expect it to be a complete description of what we observe and indeed it is not. What the model can explain well is the following:

Microwave Background

Hubble made redshift measurements of galaxies and assumed that all galaxies had roughly the same physical size. using the angular size as a measure of distance he showed there was a linear correlation between radial velocity away from the observer and the distance to the galaxy. This is called the Hubble law and the slope of the relation is the Hubble constant whose inverse represents the expansion age of the Universe.

Although the data are quite noisy, there is a general trend for more distance objects to exhibit a larger redshift. These data were sufficient to empirically demonstrate that recessional velocity was proportional to distance and hence that the Universe was in a state of uniform expansion. Einstein's General Relativity and the static Universe could now be resolved - the Universe itself was expanding. This determination of uniform, linear expansion of the Universe has a clear prediction. If galaxies are moving apart from one another today, then in the past they must have been closer together. Indeed, there must have been a time when all the galaxies in the Universe were together in the same space. At this time, the Universe was very dense and in a physical state well-removed from how it is observed to be today.

Abundance of the Light Elements

Universe at expansion age of about one second was a hot and dense mixture of electrons, protons, neutrons, neutrinoes and photons. The ratio of protons to neutrons at this time was unity as interactions with neutrinoes mediated the neutron to proton and proton to neutron conversion. However, at expansion age of 2 seconds, the Universe had cooled to the point where it became transparent to neutrinoes and this mediation was gone. Since free neutrons decay with 1/2 life of \app 900 seconds, the proton-to-neutron (P/N) ratio began to increase. As the Universe continued to expand, it cooled to the point where some the nucleons could fuse into light elements such as Deuterium and Helium through the same series of fusion reactions that are presently occuring in our Sun. At the time of this hydrogen to helium fusion P/N = 7

Making Helium:

But, deuterium is a very fragile nucleus and can easily be broken apart by a high energy photon:

Now there is an interesting race condition:

Will deuterium combine with another proton to make a nucleus with 3 nucleons or will it be photodissociated before it can do this?

This race condition depends on the density of protons:

So things are trying to proceed as follows:

The end result is the conversion of 2 protons and 2 neutrons into 1 Helium-4 nucleus.

Before the Reaction:

After the reaction

The mass of 1 Helium-4 nucleus is about 4 times the mass of a proton

Now we can make a prediction:

The helium abundance reflects three things:

Element Production beyond helium:

Previous Lecture Next Lecture Course Page