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