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Like Euclid, Riemann and Lobachevsky geometries on an almost equal footing,based on the principle of relativity of maximum symmetry proposed by Lu and thepostulate on invariant universal constants, dS/AdS SR can be set up on analmost equal footing with Einstein's SR. For dS-case, there is a coin-likerelation: A law of inertia in Beltrami atlas with Beltrami time simultaneityfor the PoR on one side. The proper-time simultaneity and a RW-like dS-spacewith entropy and an accelerated expanding S^3 fitting the cosmologicalprinciple on another. If our universe is asymptotic to the RW-like dS-space, itshould be slightly closed with an entropy bound. Contrarily, via its asymptoticbehavior, it can fix on Beltrami frames without `an argument in a circle' andacts as the origin of inertia. There is a triality of conformal extensions ofthree kinds of SR and their null physics on the projective boundary of a 5-dAdS-space. Thus there is a dS-spacetime on the boundary of a vacuum ofsupergravity. Gravity should be based on the localized PoR of full maximumsymmetry with a gauge-like dynamics. Thus, this may lead to theory of gravityof corresponding local maximum symmetry. A simple model of dS-gravitycharacterized by a dimensionless constant shows the features. Our universe mayalready indicate that the dS SR and the dS-gravity be the foundation of largescale physics.

Special Relativity and Theory of Gravity via Maximum Symmetry and Localization -- In Honor of the 80th Birthday of Professor Qikeng Lu