Age of the universe constrained from the primordial nucleosynthesis in the Brans-Dicke theory with a varying cosmological term

The age of the universe is investigated from a view-point of the primordial nucleosynthesis in the Brans-Dicke model with a varying Λ term. It is shown that the age can be long enough compared with that of the globular clusters using two critical quantities recently reported from the HST observations: the Hubble constant, and deuterium abundances. Then it is shown that the present rate of variation in the gravitational "constant" can be predicted. From the observational constraint in the primordial nucleosynthesis, the baryon density relative to the critical density is found to be Ω_b = 0.047-0.14 from the observation by Songaila et al. (1996) and Ω_b = 0.16-0.22 from that by Tytler et al. (1996), where the critical density is p_c = 6.0 × 10^-30 g cm^-3 for H₀ = 80 km s^-1 Mpc^-1 and a parameter characteristic to the Brans-Dicke theory. It is concluded that most of the matter consists of the non-baryonic dark matter if the universe is flat.