Constraints on big bang nucleosynthesis (BBN) and on cosmological parameters from conflicting deuterium observations in different high redshift QSO systems are discussed. The high deuterium observations by Carswell et al., Songaila et al., and Rugers and Hogan are consistent with ${}^4$He and ${}^7$Li observations and standard BBN ${(N}_{\nu }$ =3) and allows $N_{\nu }<~3.6$ at 95% C.L., but are inconsistent with local observations of D and ${}^3$He in the context of conventional theories of stellar and galactic evolution. In contrast, the low deuterium observations by Tytler, Fan, and Burles and Burles and Tytler are consistent with the constraints from local galactic observations, but require $N_{\nu }=1.9\mathrm{}\pm 0.3$ at 68% C.L., excluding standard BBN at 99.9% C.L., unless the systematic uncertainties in the ${}^4$He observations have been underestimated by a large amount. The high and low primordial deuterium abundances imply, respectively, ${\Omega }_B{h}^2=0.005\mathrm{}$–$0.01$ and ${\Omega }_B{h}^2=0.02\mathrm{}$–$0.03$ at 95% C.L. When combined with the high baryon fraction inferred from x-ray observations of rich clusters, the corresponding total mass densities (for $50<~H_0<~90)$ are ${\Omega }_M=0.05\mathrm{}$–$0.20$ and ${\Omega }_M=0.2\mathrm{}$–$0.7$, respectively (95% C.L.). The range of ${\Omega }_M$ corresponding to high D is in conflict with dynamical constraints $({\Omega }_{\mathrm{m}}>~0.2$–$0.3)$ and with the shape parameter constraint $(\Gamma ={\Omega }_{M}h=0.25\mathrm{}\pm 0.05)$ from large scale structure formation in CDM and $\Lambda$CDM models.

• Received 5 April 1996

DOI:https://doi.org/10.1103/PhysRevD.55.540