Abstract
Due to the recent all-sky, high-precision measurement of microwave background anisotropies by WMAP, a value for baryon-to-photon ratio eta was obtained. At the WMAP value for eta, the (HE)-H-4 abundance was predicted. In this article we use a simple semi-analytical method with He-4 predicted and measured values to place a limit on the variation of the gravitational constant G. We find using a conservative range for the measured values for Y (p), that Delta G/ G is constrained between -0.26 and 0.15. If we assume a monotonic power law time dependence G similar to t(-beta) then beta values is constrained between -0.008 and 0.0038, which translate into -2.8 x 10(-13) yr(-1) < G/ G < 6.0 x 10(-13) yr(-1). This compares well with results obtained by others using full numerical analysis.