  The general world model for homogeneous and isotropic universe has been
roposed. For this purpose, we introduce a global and fiducial system of
reference (world reference frame) constructed on a 5-dimensional space-time
that is embedding the universe, and define the line element as the separation
between two neighboring events that are distinct in space and time, as viewed
in the world reference frame. The effect of cosmic expansion on the measurement
of physical distance has been correctly included in the new metric, which
differs from the Friedmann-Robertson-Walker metric where the spatial separation
is measured for events on the hypersurface at a constant time while the
temporal separation is measured for events at different time epochs. The
Einstein's field equations with the new metric imply that closed, flat, and
open universes are filled with positive, zero, and negative energy,
respectively. We have demonstrated that the flat universe is empty and
stationary, equivalent to the Minkowski space-time, and that the universe with
positive energy density is always spatially closed and finite. In the closed
universe, the proper time of a comoving observer does not elapse uniformly as
judged in the world reference frame, in which both cosmic expansion and
time-varying light speeds cannot exceed the limiting speed of the special
relativity. We have also reconstructed cosmic evolution histories of the closed
world models that are consistent with recent astronomical observations, and
derived useful formulas such as energy-momentum relation of particles,
redshift, total energy in the universe, cosmic distance and time scales, and so
forth. It has also been shown that the inflation with positive acceleration at
the earliest epoch is improbable.
