  A general-relativistic theory of cosmology, the dynamical variables of which
are those of Hubble's, namely distances and redshifts, is presented. The theory
describes the universe as having a three-phase evolution with a decelerating
expansion followed by a constant and an accelerating expansion, and it predicts
that the universe is now in the latter phase. The theory is actually a
generalization of Hubble's law taking gravity into account by means of
Einstein's theory of general relativity. The equations obtained for the
universe expansion are elegant and very simple. It is shown, assuming
Omega_0=0.24, that the time at which the universe goes over from a decelerating
to an accelerating expansion, i.e. the constant expansion phase, occurs at
0.03tau from the big bang, where tau is the Hubble time in vacuum. Also, at
that time the cosmic radiation temperature was 11K. Recent observations of
distant supernovae imply, in defiance of expectations, that the universe growth
is accelerating, contrary to what has always been assumed that the expansion is
slowing down due to gravity. Our theory confirms these recent experimental
results by showing that the universe now is definitely in a stage of
accelerating expansion.
