Big Bang Nucleosynthesis with Variation of the “Gravitational Constant” in Presence of the “Cosmological Constant”

The “cosmological constant” being an observationally satisfactory candidate for dark energy is treated as a constant energy density of vacuum. The possible variations of both “gravitational constant” and the “cosmological constant” 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 “gravitational constant” as well as the “cosmological constant”. 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 “gravitational constant” is formed by expressing it in terms of the “cosmological constant” and the background energy density. The permitted range of the “cosmological constant” leads to that of primordial helium which has been then utilized to constrain the variation of the “gravitational constant”.