Curved Space Cosmological Bounds on the Time Variation of G

Abstract

IN a previous article¹ I gave a theoretical upper bound on the time variation of G () predicted by the Brans-Dicke (BD) theory² for Friedmann-type expanding cosmologies in flat space³. I showed that the introduction of pressure resulted in a decrease in the upper bound on . Further, it was argued (qualitatively) that the latter result holds in curved spaces as well. Although it is obviously not possible to give a rigorous proof of this without explicit knowledge of the curved space solutions, it is possible to give a much more quantitative and revealing argument in its favour. Moreover, it turns out that, independent of the exact nature of the cosmological solution, the curvature contribution to is of the same order of magnitude as the flat space contribution and adds to it or subtracts from it for positive or negative curvatures respectively.