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 viewpoint of the primordial nucleosynthesis in the Brans-Dicke model with a varying {LAMBDA} 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 {OMEGA}_b_=0.047-0.14 from the observation by Songaila et al. (1996) and {OMEGA}_b_=0.16-0.22 from that by Tytler et al. (1996), where the critical density is ρ_c_=6.0x10^-30^g/cm^3^ for H_0_=80km/s/Mpc 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.