Gravitational Lensing as a Probe of Quintessence

TL;DR

The paper assesses gravitational lensing statistics as a high-redshift probe of a time-varying dark energy equation of state, parameterized by $w(z) \approx w_{0} + z (dw/dz)_{0}$. It develops a Fisher-matrix forecast using the redshift distribution of lensed quasars from SDSS, including magnification bias and selection effects, to constrain $w_{0}$ and $(dw/dz)_{0}$ in a flat universe. The study shows that SDSS-scale data could yield thousands of lensed quasars with redshifts up to $z\sim5$, enabling meaningful constraints on dark-energy dynamics, though results depend on the fiducial model (notably when $w_{0} + z (dw/dz)_{0} \sim -1$). Overall, lensing provides a complementary approach to SN Ia and CMB for probing quintessence and ruling out certain models or a pure cosmological constant.

Abstract

A large number of cosmological studies now suggest that roughly two-thirds of the critical energy density of the Universe exists in a component with negative pressure. If the equation of state of such an energy component varies with time, it should in principle be possible to identify such a variation using cosmological probes over a wide range in redshift. Proper detection of any time variation, however, requires cosmological probes beyond the currently studied range in redshift of $\sim$ 0.1 to 1. We extend our analysis to gravitational lensing statistics at high redshift and suggest that a reliable sample of lensed sources, out to a redshift of $\sim$ 5, can be used to constrain the variation of the equation of state, provided that both the redshift distribution of lensed sources and the selection function involved with the lensed source discovery process are known. An exciting opportunity to catalog an adequate sample of lensed sources (quasars) to probe quintessence is now available 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 state today $w_0$ and its rate of change $(dw/dz)_0$ can simultaneously be constrained. Such a determination can rule out some missing-energy candidates, such as classes of quintessence models or a cosmological constant.