Constraining dark energy from the abundance of weak gravitational lenses
  We examine the prospect of using the observed abundance of weak gravitational lenses to constrain the equation-of-state parameter w of the dark energy. Here we solve the spherical-collapse model with dark energy, clarifying some ambiguities found in the literature, and provide fitting formulas for the overdensity at virialization and the linear-theory overdensity at collapse. We then compute the variation in the predicted weak-lens abundance with w. We find that the predicted redshift distribution and number count of weak lenses are highly degenerate in w and \Omega_0. If we fix \Omega_0 the number count for w=-2/3 is a factor of 2 smaller than for the \LambdaCDM model. However, if we allow \Omega_0 to vary with w such that the amplitude of the matter power spectrum as measured by COBE matches that obtained from the X-ray cluster abundance, the decrease in the predicted lens abundance is less than 25% for -1 < w < -0.4. We show that a more promising method for constraining the dark energy---one that is largely unaffected by the \Omega_0 - w degeneracy as well as uncertainties in observational noise---is to compare the relative abundance of virialized X-ray lensing clusters with the abundance of non-virialized, X-ray underluminous, lensing halos. For aperture sizes of 15 arcmin, the predicted ratio of the non-virialized to virialized lenses is greater than 40% and varies by 20% between w=-1 and w=-0.6. Overall, if all other weak lensing parameters are fixed, a survey must cover > 40 degree^2 in order for the number count to differentiate a \LambdaCDM cosmology from a w=-0.9 model to 3\sigma. However, given uncertainties in the lensing parameters, the non-virialized lens fraction provides the most robust constraint on w, requiring 50 degree^2 of sky coverage in order to differentiate w=-1 from w=-0.6 to 3\sigma. 
Nevin N. Weinberg, Marc Kamionkowski (Caltech)