The accelerating universe is the observation that the universe appears to be expanding at an increasing rate, which in formal terms means that the cosmic scale factor a(t) has a positive second derivative, implying that the velocity at which a given galaxy is receding from us should be continually increasing over time (here the recession velocity is the same one that appears in Hubble's law; defining 'velocity' in cosmology is somewhat subtle, see Comoving distance#Uses of the proper distance for a discussion). In 1998 observations of Type Ia supernovae suggested that the expansion of the universe has been accelerating since around redshift of z~0.5.
In the past few years, these observations have been corroborated by several independent sources: the cosmic microwave background radiation and large scale structure, age of the universe, as well as improved measurements of the supernova, and X-ray properties of galaxy clusters.
An expanding universe means that density drops due to continual space being added between all matter. If acceleration continues, eventually all galaxies beyond our own Local supercluster will redshift so far that it will become hard to detect them, and the distant universe will turn dark.
Models attempting to explain accelerating expansion include some form of dark energy: Cosmological Constant, Quintessence, Dark Fluid or Phantom energy. The latest WMAP data favours the cosmological constant. The most important property of dark energy is that it has negative pressure which is distributed relatively homogeneously in space.
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