Robert V Wagoner An initial impact of the CMBR on nucleosynthesis in big and little bangs

Bob Wagoner is Professor of Physics, Emeritus, Stanford University. A continuing research interest is the physics of compact objects, including their roles as sources of gravitational radiation detectable by LIGO and other facilities.

Timing may not be everything, but it certainly can help. In 1960, when I was a mechanical engineering undergraduate at Cornell, I attended the Messenger Lectures of Fred Hoyle on cosmology. That experience, and books such as Dennis Sciama's (1959) The Unity of the Universe, opened my mind. I received my PhD in physics at Stanford in 1965. My thesis was on general relativity, although I spent part of one summer working (amid many spiders) on Ron Bracewell's radio telescopes. I was on my way to a research fellowship at Caltech just as the discovery of Penzias and Wilson (1965a)

was announced. Soon after my arrival, Willy Fowler invited me to join him and Fred in an exploration of the consequences of this sea of photons, using nuclear astrophysics as a cosmological probe.

Details of my view of the development of primeval nucleosynthesis through 1973 can be found in a review (Wagoner 1990), where references that I have omitted here can be found. In keeping with the scope of this volume, my focus here will be mainly on the 1960s.

However, I begin by mentioning the first prediction of a cosmic radiation temperature (5K) by Ralph Alpher and Robert Herman (1948), based on their work with George Gamow on what is now called big bang nucleosynthesis. It may not be well known that they neglected the overwhelming influence of neutrinos in establishing the neutron-proton ratio (and thus the synthesis of heavier nuclei), so that the approximate agreement with the eventual observation was fortuitous. Hayashi (1950) provided the correct interaction rates, and Alpher, Follin and Herman (1953) provided the first complete description of the standard model of the evolving major constituents (but no baryons except protons and neutrons) of the early universe.

It is somewhat of a mystery why this knowledge was not employed to recalculate the abundances until Zel'dovich (1963a) and Hoyle and Tayler (1964) considered the production of the key nucleus, helium (4He). Fermi and Turkevich had developed a nuclear reaction network just before 1950. Zel'dovich concluded that a reasonable production of helium required that the present temperature of the fossil radiation is high (20 K), apparently because he believed indications of a low observed primordial abundance of helium (see the contribution by Novikov on page 99). This led him to (temporarily) abandon the big bang model.

Hoyle and Tayler provided more details of their (approximate but realistic) calculation, showing that the neutron-proton ratio when the weak interactions "froze out" essentially determined the abundance of helium, which was weakly dependent on the photon-baryon ratio. They noted, however, that conditions within exploding supermassive stars could be similar to that in the early universe (but with fewer photons per baryon). They also noted that the observed energy density of starlight only required the production of 10% of the observed amount of helium. Thus they concluded "that most, if not all, of the material of our everyday world has been 'cooked' to a temperature in excess of 1010 K." It also may not be widely known that they were the first to note that the number of types of neutrinos affects the expansion rate and thus the abundance of helium.

I was very fortunate to be a postdoctoral fellow (1965-1968) in Caltech's Kellogg Lab when it was a major hotbed of theoretical astrophysics. The emerging revelations of the nature of quasars only added to the excitement produced by the realizations of the consequences of the cosmic microwave radiation. The enthusiasm of Willy Fowler for many aspects of science and life (parties, etc.) infected everyone.

In our collaboration, Fred's point of view was of course influenced by his continuing belief in the steady state universe and thus the production of helium and other light elements within exploding supermassive stars (which we dubbed "little bangs"), complementing the ordinary stellar production (Burbidge et al. 1957; Cameron 1957) of the heavier elements. However, he was also impressed by the fact that if the helium was produced mainly by ordinary stars and their resulting luminosity was somehow universally thermalized at a time close to the present epoch, the radiation temperature would be close to 3 K.

The most critical element in my computer code was the nuclear reaction data provided by Willy and his group and many other nuclear physicists. Of course, we also had to extrapolate or otherwise estimate the rates of a few reactions that had not been measured at the relevant effective energies (usually 0.1-0.5 MeV, except for neutrons).

I presented our first results at the April 1966 annual meeting of the National Academy of Sciences (Wagoner, Fowler and Hoyle 1966). The calculation involved 40 nuclei and 79 nuclear and weak reactions. At about the same time, Jim Peebles published his calculation of the abundances of helium and deuterium within both the standard model and universes with different expansion rates (Peebles 1966). The accuracy of his predictions of the abundance of 2H and 3He was reduced by the limited number of nuclear reactions included.

Our results were published the following year (Wagoner, Fowler and Hoyle 1967). As indicated above, we considered a large range of the baryon-photon ratio, corresponding to big and little bangs. Our major conclusion was that reasonable agreement with observed abundances of 2H, 3He, 4He, and 7Li could be achieved if the universal baryon (matter) density was about 2 x 10"31 gcm-3 (a factor of 2 less than the presently accepted value from WMAP and other data sets; Spergel et al. 2007). However, the abundance data that was available was from within the Solar System (Earth, Sun, and meteorites), so we did not know how relevant it was. On the other hand, the predicted abundances have stood the test of time. We also explored the effects of inhomogeneity and neutrino degeneracy (large lepton-photon ratios). Within little bangs (larger baryon-photon ratios), carbon and heavier nuclei were produced, but the abundances did not closely resemble those observed unless the bounce occurred at a temperature of about 109 K. Fred believed that this could happen in the first generation of (supermassive) stars (usually termed "Pop III stars," after the classification of stellar populations into the younger Pop I and the older Pop II).

My summer of 1967 (and 1971) at Fred's new Institute of Theoretical Astronomy at Cambridge was very memorable. Willy, Don Clayton, and I occupied the first "office" in the hut in the sheep pasture behind the present Institute. The only building housed the IBM 360-44 computer, which I had to myself a large part of the time to tune my nucleosynthesis code. Many discussions with Fred focused on the properties of supermassive stars (sometimes over martinis while watching cricket), and with Willy and the Burbidges on abundance issues.

My involvement in nuclear astrophysics essentially ended a decade later. Exploration of other big bang models (Wagoner 1967, 1973), including the results of Peebles (1966) and those within anisotropic universes (Hawking and Tayler 1966; Thorne 1967), revealed to me that in general, only three factors affected the abundances produced. They were

(i) The number of baryons per photon.

(ii) The expansion rate, dependent upon the theory of gravity, anisotropy, and other forms of mass-energy density (other neutrino types, gravitational radiation, magnetic fields, etc.).

(iii) The neutron-proton ratio, dependent upon the lepton (neutrino) number per photon and the neutrino phase-space distribution (if the expansion was anisotropic).

The agreement of the abundance of 4He with that produced within the standard model, and the detection of interstellar deuterium (Rogerson and York 1973) then strongly supported the conclusion that the density of ordinary matter was far short of that required for a flat universe. It was very gratifying that the early universe produced precisely those nuclei that stars or cosmic ray spallation could not.

The power of this deep probe of the early universe is based upon the fact that its physics is known, from the heroic efforts of many nuclear physicists (Fowler, Caughlan and Zimmerman 1967, 1975) and the discovery and subsequent measurements of the blackbody flux of cosmic microwave radiation.

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