Dark Energy: Mystery of the Millennium

Nearly seventy per cent of the energy density in the universe is unclustered and exerts negative pressure. This conclusion — now supported by numerous observations — poses the greatest challenge for theoretical physics today. I discuss this issue with special emphasis on the cosmological constant as the possible choice for the dark energy. Several curious features of a universe with a cosmological constant are described and some possible approaches to understand the nature of the cosmological constant are reviewed. In particular, I show how some of the recent ideas, related to a thermodynamic route to gravity, allow us to: (i) create a paradigm in which the bulk value of cosmological constant is irrelevant and (ii) obtain the correct, observed, value for the cosmological constant from vacuum fluctuations in a region confined by the deSitter horizon. Keywords: cosmological constant, dark energy, Einstein-Hilbert action, Gauss-Bonnet, Holography 1. THE RISE OF THE DARK ENERGY: BRIEF HISTORY The cosmological data of exquisite quality, which became available in the last couple of decades, have thrusted upon us a rather preposterous composition for the universe which defies any simple explanation, thereby posing the greatest challenge theoretical physics has ever faced. It is conventional to measure the energy densities of the various species which drive the expansion of the universe in terms of a critical energy density ρc = 3H 2 0 /8πG where H0 = ( ˙a/a)0 is the rate of expansion of the universe at present. The variables Ωi = ρi/ρc will then give the fractional contribution of different components of the universe (i denoting baryons, dark matter, radiation, etc.) to the critical density.