On the measure of spacetime and gravity

Abstract

By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time) that requires not only a universally constant invariant velocity but also an invariant length given by its constant curvature, $Λ$ and spacetime is completely free of dynamics. Thus $c$ and $Λ$ are the only two true constants of the spacetime structure and no other physical constant could claim this degree of fundamentalness. When matter is introduced, the spacetime becomes inhomogeneous and dynamic, and its curvature then determines by the Bianchi differential identity the equation of motion for the Einstein gravity. The homogeneity thus demands that the natural state of \textit{free spacetime} is of constant curvature and the cosmological constant thus emerges as a clear prediction which seems to be borne out by the observations of accelerating expansion of the Universe. However it has no relation to the vacuum energy and it could be envisioned that in terms of the Planck area the Universe measures $10^{120}$ units!