Wednesday, 27 October 2010

Physics Projects 1 Big Bang

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

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.

When all that is under my belt, I can start given the guidelines in Kawano's manual writing my own code.

So if I'm lucky this project should see completion in the next 2-3 years but I do have to stop procrastinating.


  1. I suppose this means you firmly 'believe' in the Big Bang? I have, recently, seen an episode of Horizon. I think it was 'What happened before the Big Bang?'. It was mainly about theoretical physicists expressing their doubts about the Big Bang theory. - Can anything be sure, besides in mathematics? I doubt it.

  2. well I'm really only concerned with what happened 100th of a second from what is called the big bang to the 1st 3 minutes. None of the speculation about what happened before that will affect this. This seems fairly well established physics and it is that I want to concentrate on. The prediction of the Hydrogen Helium abundance is fairly robust which is why the simple approximation I outlined above gets pretty close to the correct answer. What happened before as that Horizon program showed is anyones guess. The only slight cloud on the horizon is the prediction of the Lithium abundance. Anyway before I criticise the established view I want to understand it.
    As for surety in mathematics well thats a very interesting question given Godel's theorem. Yes one can be sure of logical deductions from a set of axioms but what is the basis for those axioms ?

  3. Chris, one of the interesting differences between now and when Peebles did his calculations is that, as you know, we now think that omega, the density parameter, is 1 and this is largely due to dark matter and dark energy, and not due to baryons as Peebles had assumed. This must alter the calculations in some way. You have a low density of material that is undergoing nuclear synthesis (the baryons) whilst at the same time this is going on in an environment which is gravitationally more compact (due to omega being 1). I would be interested to know how this affects the primordial abundances.


  4. Hi Duncan I'm not really sure the critical density plays that much of a part in the baryonic abundances. The key parameter is the rate of expansion and the neutron decay rate which has changed by about 10% downwards since Peebles did his original calculation. All that stuff about the critical density applies before the first 100th of a second. The main difference of course is that Peebles thought they had accounted for all the matter in the universe whereas we now know that it only accounts for 4% of it.

  5. To further add to the above comment In the period I'm interested baryonic matter has decoupled from Dark matter and Dark energy, so it can carry on independently of the other components as by definition dark matter and dark energy do not interact with baryonic matter. Certainly the books and papers I'm looking don't make any reference to the critical density in this phase.

  6. For those in the UK:
    Outside the UK: ( Search for Horizon Big Bang, both HD, non-HD version available )