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. In this paper a
general-relativistic cosmological theory that gives a direct relationship
between distances and redshifts in an expanding universe is presented. The
theory is actually a generalization of Hubble's law taking gravity into account
by means of Einstein's theory of general relativity. The theory predicts that
the universe can have three phases of expansion, decelerating, constant and
accelerating, but it is shown that at present the first two cases are excluded,
although in the past it had experienced them. Our theory shows that the
universe now is definitely in the stage of accelerating expansion, confirming
the recent experimental results
