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On Beltrami Model of de Sitter Spacetime
Based on some important properties of space, we present a Beltrami model
that may shed light on the observable puzzle of space
and the paradox between the special relativity principle and cosmological
principle. In , there are inertial-type coordinates and
inertial-type observers. Thus, the classical observables can be defined for
test particles and light signals. In addition, by choosing the definition of
simultaneity the Beltrami metric is transformed to the Robertson-Walker-like
metric. It is of positive spatial curvature of order . This is more or
less indicated already by the CMB power spectrum from WMAP and should be
further confirmed by its data in large scale.Comment: 4 page
Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
Between Snyder's quantized space-time model in de Sitter space of momenta and
the \dS special relativity on \dS-spacetime of radius with Beltrami
coordinates, there is a one-to-one dual correspondence supported by a minimum
uncertainty-like argument. Together with Planck length , should be a fundamental constant. They lead to a
dimensionless constant . These indicate that physics at these two scales should be dual to
each other and there is in-between gravity of local \dS-invariance
characterized by . A simple model of \dS-gravity with a gauge-like action on
umbilical manifolds may show these characters. It can pass the observation
tests and support the duality.Comment: 32 page
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