  In the late 1990s, observations of type Ia supernovae led to the astounding
discovery that the universe is expanding at an accelerating rate. The
explanation of this anomalous acceleration has been one of the great problems
in physics since that discovery. We propose cosmological models that can simply
and elegantly explain the cosmic acceleration via the geometric structure of
the spacetime continuum, without introducing a cosmological constant into the
standard Einstein field equation, negating the necessity for the existence of
dark energy. In this geometry, the three fundamental physical dimensions
length, time, and mass are related in new kind of relativity. There are four
conspicuous features of these models: 1) the speed of light and the
gravitational constant are not constant, but vary with the evolution of the
universe, 2) time has no beginning and no end; i.e., there is neither a big
bang nor a big crunch singularity, 3) the spatial section of the universe is a
3-sphere, and 4) in the process of evolution, the universe experiences phases
of both acceleration and deceleration. One of these models is selected and
tested against current cosmological observations, and is found to fit the
redshift- luminosity distance data quite well.
