Big-bang nucleosynthesis in Brans-Dicke cosmology with a varying $\Lambda$ term related to WMAP

We investigate the big-bang nucleosynthesis in a Brans-Dicke model with a varying $\Lambda$ term using the Monte-Carlo method and likelihood analysis. It is found that the cosmic expansion rate differs appreciably from that of the standard model. The produced abundances of $^4$He, D, and barely Li are consistent with the observed ones within the uncertainties in nuclear reaction rates when the baryon to photon ratio $\eta = (5.47 - 6.64)\times 10^{-10}$, which is in agreement with the value deduced from WMAP.