The Big-Bang Nucleosynthesis Limit to the Number of Neutrino Species

Concern about systematic uncertainty in the He abundance as well as the chemical evolution of He leads us to re-examine this important limit. It is shown that with conservative assumptions no more than the equivalent of 4 massless neutrino species are allowed. Even with the most extreme estimates of the astrophysical uncertainties a meaningful limit still exists, less than 5 massless neutrino species, and illustrates the robustness of this argument. A definitive measurement of the deuterium abundance in high-redshift hydrogen clouds should soon sharpen the limit. Introduction. Big-bang nucleosynthesis is one of the experimental pillars of the standard cosmology [1, 2]. It also probes particle physics. Among other things, it has been used to set a stringent limit to the energy density contributed by light (mass ≪ MeV) particle species, usually quantified as the equivalent number of massless neutrino species (≡ Nν) [3]. This limit indicated that the number of neutrino species was small before accelerator experiments were able to experimentally establish this directly, and further, has served to constraint theories proposed to unify the forces and particles of Nature. Since the cosmological bound also constrains light species that do not couple to the Z, it is an important complement to the LEP measurement, Nν = 2.991± 0.016. The physics underlying the neutrino limit is simple: the big-bang production of He increases with both baryon density (quantified by the present baryon to photon ratio η) and the number of massless neutrino species. Thus, an upper limit to the primeval He abundance (≡ YP ) and a lower limit to the baryon density lead to an upper limit to Nν . The lower limit to the baryon density is based upon the big-bang production of deuterium, which rises rapidly with decreasing baryon density [4]. Because D is easily destroyed in stars, first being burnt to He, the limit actually hinges upon D + He, bringing in the chemical evolution of He. This has been the standard approach for setting a limit to Nν . Over the past five years limits to Nν ranging from 3.04 to around 5 have been quoted [5]. The disparity arises because the irreducible uncertainties are systematic, rather than statistical. In particular, the pressing issues involve the primeval abundance of He and the chemical evolution of He (astronomers use the term “chemical evolution” to refer to nuclear processing). The purpose of this paper is to clarify the current situation, to use a new technique to obtain a limit to Nν that is independent of the chemical evolution of He, and to show how measurements of the primeval D abundance in high-redshift hydrogen clouds should soon sharpen the neutrino limit. In so doing, we will emphasize the robustness of the cosmological limit to Nν . The light-element abundances. To orient the reader we begin with a brief overview. The big-bang production of D, He, He and Li is summarized in Fig. 1. The predicted and measured abundances are consistent—within the uncertainties—for η ≃ (2 − 7) × 10 [1, 6]. The status of the four light elements is as follows. 1. The lithium abundance is measured in the atmospheres of the oldest stars in our galaxy (pop II halo stars) and is relatively well determined, (Li/H)pop II = (1.4±0.3)×10 −10 [1, 7]. Because Li burns at a low temperature, the most important concern is that Li may have been depleted. Stellar models indicate that a depletion of up to a factor of about two is consistent with the observations of Li and other light elements in these old stars [8]. 2. The He abundance increases with time, as He is made by stars, and so any measurement provides an upper bound to the primeval component. The primeval abundance is extrapolated from measurements of metal-poor, extragalactic HII regions (hot clouds of ionized H and He gas). A compilation and analysis of the extant data gave