%0 Journal Article %T Big Bang Nucleosynthesis with Variation of the ˇ°Gravitational Constantˇ± in Presence of the ˇ°Cosmological Constantˇ± %J International Journal of Astronomy %@ 2169-8856 %D 2012 %I %R 10.5923/j.astronomy.20120102.01 %X The ˇ°cosmological constantˇ± being an observationally satisfactory candidate for dark energy is treated as a constant energy density of vacuum. The possible variations of both ˇ°gravitational constantˇ± and the ˇ°cosmological constantˇ± during the early Universe have been constrained by Big Bang Nucleosynthesis (BBN). The BBN is highly sensitive to the early Universe expansion rate which is in fact governed by the ˇ°gravitational constantˇ± as well as the ˇ°cosmological constantˇ±. It manifests in the variation of primordial elemental abundances for helium ( and lithium (, through elevation of the neutron-proton freeze-out temperature. Such elevation is equivalent to diminution of neutron-proton mass difference (Q). An effective ˇ°gravitational constantˇ± is formed by expressing it in terms of the ˇ°cosmological constantˇ± and the background energy density. The permitted range of the ˇ°cosmological constantˇ± leads to that of primordial helium which has been then utilized to constrain the variation of the ˇ°gravitational constantˇ±. %K Gravitational Constant %K Cosmological Constant %K Freeze-Out %K Vacuum Energy %U http://article.sapub.org/10.5923.j.astronomy.20120102.01.html