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, $\Lambda$ and spacetime is completely free of dynamics. Thus $c$ and $\Lambda$ 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!

5 pages, revtex, Received Honorable Mention in the 2011 Gravity Research Foundation Awards for Essays on Gravitation

References in corpus (3)

• Dark Energy and Gravity
• de Sitter special relativity
• Indications of de Sitter Spacetime from Classical Sequential Growth Dynamics of Causal Sets

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• Stability and existence analysis of static black holes in pure Lovelock theories
• Is "Dark Energy" a Quantum Vacuum Energy?
• Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime
• Non-perturbative analysis for a massless minimal quantum scalar with $V(\varphi )=\lambda {\varphi }^4/4!+\beta {\varphi }^3/3!$ in the inflationary de Sitter spacetime
• Understanding General Relativity after 100 years: A matter of perspective
• Cleaning up the cosmological constant
• Resummation of local and non-local scalar self energies via the Schwinger-Dyson equation in de Sitter spacetime
• Normal coordinates based on curved tangent space
• Cosmological Mass of the Photon and Dark Energy as its Bose-Einstein Condensate in de Sitter Space
• Fundamental forces and their dynamics
• Dark Energy From The Gravity Vacuum