Gravitational Lensing as a Probe of Quintessence

A large number of cosmological studies now suggest that roughly two-thirds ofthe critical energy density of the Universe exists in a component with negativepressure. If the equation of state of such an energy component varies withtime, it should in principle be possible to identify such a variation usingcosmological probes over a wide range in redshift. Proper detection of any timevariation, however, requires cosmological probes beyond the currently studiedrange in redshift of $\sim$ 0.1 to 1. We extend our analysis to gravitationallensing statistics at high redshift and suggest that a reliable sample oflensed sources, out to a redshift of $\sim$ 5, can be used to constrain thevariation of the equation of state, provided that both the redshiftdistribution of lensed sources and the selection function involved with thelensed source discovery process are known. An exciting opportunity to catalogan adequate sample of lensed sources (quasars) to probe quintessence is nowavailable with the ongoing Sloan Digital Sky Survey. Writing $w(z)\approx w_0 +z (dw/dz)_0$, we study the expected accuracy to which the equation of statetoday $w_0$ and its rate of change $(dw/dz)_0$ can simultaneously beconstrained. Such a determination can rule out some missing-energy candidates,such as classes of quintessence models or a cosmological constant.Comment: Accepted for publication in ApJ Letters (4 pages, including 4 figures