Outside of my OU work I have a number of physics projects I have been working on, on and off over the past 20 years or so. This post outlines my plan to fully understand the establishment of the big bang model in the late 1960's to early 1970's. When life was relatively simple and there was no dark matter, dark energy and only one universe to worry about. Open any book on cosmology, popular or otherwise and in the section entitled Big Bang Nuclear synthesis (BBN for short) there will be a couple of graphs plotted showing the abundances of Helium and Hydrogen as they evolved in time from about 100th of a second to about 3 minutes after the big bang. Another graph will show the abundances of other light elements such as Lithium and Beylium. However what they will not tell you in any great detail is how these graph's were obtained. In those crucial moments the temperature of the universe (according to the story) was such that stable nuclei were able to be formed and in a few minutes all of the Hydrogen and Helium that we observe in the universe was created. The person who was able to synthesise his knowledge of both nuclear physics, statistical physics and cosmology to give a coherent story which fits the facts was P J E Peebles ('Primordial Helium abundance and the Primordial Fireball II Astrophysical Journal 146 pp 545-552 1966). The significance, as readers of this blog will probably know, is that a number of cosmologists such as Fred Hoyle and Hermann Bondi had hoped that they could account for the Hydrogen and Helium abundances from Stellar explosions. Peebles calculation was what physicists//engineers refer to as a back of the envelope calculation and it wasn't long before more sophisticated calculations, based ironically on the codes that Hoyle had written to study stellar explosions were able to come up with more accurate predictions. This line of research culminated with the work of Kawano in the early 1990's with a code written in FORTRAN (like all good scientific codes) which considers a staggering 88 basic nuclear reactions and is able to predict the abundances of all the light elements based on a knowledge of their reaction rates, a general relativistic cosmological model and relativistic statistical physics. Kawano's manual for the code he wrote is accessible from Fermi lab
http://lss.fnal.gov/archive/test-preprint/fermilab-pub-92-004-a.shtml
and it is one of my long term ambitions to put all the pieces together in one place concentrating in detail on all the in's and out's of the calculation and culminating in my own code which is able to reproduce at least in rough outline the same results that Peeble's got. Now that I have a bit of spare time between courses I hope to be able to give this project a well deserved kick up the backside and rejuvenate it.
The current status is as follows
1) A general overview based on a classical approximation. (status Complete)
Some what bizarrely a good approximation to the results of Peeble's can be obtained on the basis of Newtonian Physics and classical statistical physics as enshrined in the Boltzmann distribution. I have summarised this work in a word document which provides a good overview hopefully understandable by anyone who has completed MS221 and possible S207. If people would like a copy please request one from my home e-mail
The core background to understand the calculation fully draws on three main topics
a) General Relativity and it's application to Cosmology in particular the Friedmann equations.
b) Fermi's theory of the Weak Interaction and a calculation of the Nuclear Decay rate which is the key parameter in the theory. One can always cheat by just quoting the experimental value, however one misses out on a key insight as to how particle physics and Cosmology combine together.
c) Relativistic Statistical Physics
I've more or less completed some notes on neutron decay and I've got backgtound notes on General Relativity my aim over the next couple of months is to tidy these notes up and then make a start on relativistic statisitical physics. Statistical physics has never been one of my strong points when I was at Exeter a certain Dr Jones tried to teach our class it, but he taught it in an idiosyncratic manner to say the least and so I was always put off it. I hope to remedy this.
So if I'm lucky this project should see completion in the next 2-3 years but I do have to stop procrastinating.
