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Deuteronomy and Numbers

Determining the amount of matter in the Universe today is difficult. Matter is scattered about in bright stars, dust, gas, planets, faint stars, white dwarfs and black holes. The nuclear reactor that was the Universe at an age of one second provides another approach, albeit unconventional.

When the Universe was a second old, ordinary matter existed in the form of uniformly scattered neutrons and protons. By the time the Universe was 200 seconds old, nuclear reactions had produced He-4 (24%), D (parts in 105 relative to H), He-3 (same as D) and Li (parts in 1010), with the bulk of the protons left burned. The yields of this cosmic reactor depend upon the average density of matter. While the bulk of the nuclei produced are He-4, it is the yield of Deuterium that is most sensitive to the density of matter; for that reason, Schramm and Turner call it the baryometer (“baryon meter,” ref 1).

Shortly after the microwave background was discovered in 1965, the details of big-bang nucleosynthesis were worked out in detail. David Schramm was one of the first to realize that D was a sensitive indicator of the baryon density (ref 2, written when Schramm was a graduate student at Caltech). A few years later, after arriving at the University of Chicago, he wrote a seminal paper which argued that since the big bang deuterium has only been destroyed in stars and elsewhere (ref 3). This means that the big bang must produce at least as much D as we see today (in fact, the present abundance of deuterium in the solar neighborhood is about a factor of two smaller than the amount the big bang produced). The earliest measurement of D was made by the Apollo astronauts who used a foil on the moon exposed to solar-wind particles (ref 4; actually, they measured He-3; D in the sun is burnt to He-3). Later, York and Rogerson used the Copernicus satellite to make the first measurement of the D abundance in the local ISM, by measuring the amount of UV light that was absorbed by D in the ISM in the starlight of nearby, hot young stars (ref. 5).

These two measurements set a lower limit to the amount of D produced in the big bang; since the amount of deuterium produced in the big bang decreases with the density of baryons, this in turns leads to an upper limit to the amount of ordinary matter. Until 1998 that upper limit stood at about 10 percent of the critical density. This limit was crucial to the case for exotic dark matter in the Universe: the amount of dark matter needed to hold structures in the Universe together, now believed to be about 35 percent of the critical density, was greater than this.

In 1976 a young assistant professor at Chicago, Tom Adams, outlined a technique for determining the primeval abundance of Deuterium (ref 6). He proposed using high-redshift quasars to “X-ray” intergalactic gas clouds of primordial material. Such clouds are “seen” by the amount of light they absorb from the quasar; since D and ordinary H absorb at slightly different wavelengths, both can be measured. In Adams' paper he thanks Schramm for pointing out the importance of the primordial deuterium abundance for determining the baryon density.

Adams' dream took 22 years and the light-collecting power of the 10-meter Keck telescope to be realized. David Tytler and his then-graduate student Scott Burles made the first definitive measurement of the D abundance in a very distant and very primitive gas cloud (ref 7). Since then, Tytler, Burles (who went on to a postdoctoral position at Chicago and then a staff position at Fermilab) and others have measured the deuterium abundance in other pristine samples of cosmic gas and obtained similar values (refs. 8 and 9).

To use the deuterium abundance to determine the amount of ordinary matter in the Universe requires accurate theoretical predictions for its big-bang production. Schramm and his colleagues at Chicago (as well as scientists elsewhere) have refined the calculations. From the Tytler/Burles deuterium measurement and the Chicago calculations one infers: density of ordinary matter = 3.8 x 10-31 g/cc with a 5 percent margin of error (in terms of the fraction of critical density, that corresponds to 4 percent ±0.2 of critical density, for a Hubble constant of 70 km/sec/Mpc)).

David Schramm's last paper was written just after the first measurements of the primeval deuterium abundance realized a career-long dream (ref 1). Titled “BBN Enters the Precision Era,” he and Turner pointed to a critical test of the BBN prediction for the baryon density: comparing it with an independent determination based upon the measurements of the cosmic microwave background radiation. That is the result being reported today by the DASI team, 4.5 percent of the critical density with a margin of error of ±0.8 percent.

The agreement between measures of the amount of ordinary matter is simply stunning. The underlying physics is completely different: nuclear reactions occurring at one second and matter compressing photons as it fell into dark matter potential wells when the Universe was 400,000 years old. This test of the BBN baryon density realizes Schramm's dream, is a key consistency test of the big bang and makes the case for exotic dark matter almost airtight.


Key references:
  1. D. Schramm and M. Turner, Rev Mod Phys 70, 303 (1998)
  2. H. Reeves, J. Audouze, W. Fowler and D. Schramm, ApJ 179, 909 (1973)
  3. R. Epstein, J. Lattimer and D. Schramm, Nature 263, 198 (1976)
  4. J. Geiss et al, J. Geophys. Res. 75, 5972 (1970)
  5. J. Rogerson and D. York, ApJ 186, L95 (1973)
  6. F.T. Adams, A&A 50, 461 (1976)
  7. S. Burles & D. Tytler, ApJ 507, 732 (1998); ApJ 499, 699 (1998).
  8. D. Tytler et al (Nobel Symposium), Phys. Scr. T85, 12 (2000)
  9. J. O'Meara et al, ApJ, in press (2001) (astro-ph/0011179)
  10. S. Burles, K. Nollett and M. Turner, PRD 63, 063512 (2001)
  11. K. Olive, G. Steigman, and T.P. Walker, Phys Rep 333, 389 (2000)

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