Perhaps the greatest surprise in cosmology since Edwin Hubble's original discovery of the expansion of the universe in the 1930s has been the compelling evidence that the rate of cosmic expansion has been accelerating rather than slowing down in the past few billion years. Before 1998, models of an accelerating universe were very unfashionable; following General Relativity, cosmic acceleration appeared to require the cosmos to be dominated by energy with negative pressure or by Einstein's admitted “greatest blunder”– the cosmological constant, Λ. However, the magnitude of the cosmological constant required just to accelerate the cosmos today is 120 orders of magnitude smaller than the natural quantum gravity scale set by the Planck mass, which would make it the single worst theoretically estimated quantity in the history of science! But in 1998, contrary evidence turned cosmology on its head. Two independent teams showed that distant supernovae were fainter and hence more distant than could be explained in a decelerating universe, thereby forcing cosmologists to confront the possibility of acceleration. Since then, evidence for acceleration has steadily mounted and improved, yet our knowledge of the underlying physics of the process has gone almost nowhere. We still do not know whether Einstein's theory of gravity is wrong, whether the acceleration is caused by the cosmological constant or by a completely new form of matter such as the scalar fields often invoked (but as yet undetected) as sources of acceleration during the first few fractions of a second after the Big Bang. Deciding between these three possible sources of acceleration is one of the major goals of cosmology in the next decade, with scores of dedicated surveys and experiments planned or in progress attempting to address the nature of “dark energy”, as the mysterious source of acceleration is called. There are several major new supernovae searches (ESSENCE, SNLS, SDSS-II) that, by 2008, will enhance our understanding of dark energy by measuring the distances to several hundred new Type Ia supernovae (SNIa) (Matheson et al. 2005; Mullivan 2005; Sako 2005). SNIa measurements are, however, fundamentally limited by the fact that we do not physically understand the mechanisms of supernova explosion. Also there are many possible astrophysical uncertainties, such as progenitor bias, absorption of emitted photons by intervening dust and possible redshift evolution of SNIa. In addition, SNIa distance measurements are not ideal dark energy discriminators because, given a dark energy model, one must perform two integrals over redshift to derive the corresponding predicted distance (to compare with the observed distance provided by the SNIa). This double integral smears out any interesting or distinctive fingerprints of the underlying physics, implying that one needs a very large number of SNIa to be able to differentiate between different dark energy models. This is exactly the plan with future SNIa surveys such as the Large Synoptic Survey Telescope (LSST), Dark Energy Survey (DES) and the SuperNova Acceleration Probe (SNAP), a satellite mission that would fly after 2014 and would detect nearly 2000 SNIa in the redshift range 0 < z < 1.7. An alternative and highly profitable approach is to measure the Hubble expansion rate, as a function of redshift, i.e. H(z). This would be advantageous since H(z) is linked to the dark energy models through a single redshift integral only, making model discrimination easier. Measuring H(z) is ambitious, however. It has taken decades of heated debate to reach a consensus for the local (i.e. z= 0) value, H0, of this rate. How can we therefore hope to track the evolution of H with time? We will show that new methods will not only detect H(z), but measure it to an accuracy of less than 3% at certain redshifts, significantly better than we know its value at z= 0, i.e. today
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