Constraints on Cosmological Parameters from Strong Gravitational Lensing by Galaxy Clusters

Abstract

We investigate how observations of strong lensing can be used to infer cosmological parameters, in particular the equation of state of dark energy. We focus on the growth of the critical lines of lensing clusters with the source redshift as this behaviour depends on the distance-redshift relation and is therefore cosmologically sensitive. Purely analytical approaches are generally insufficient because they rely on axisymmetric mass distributions and thus cannot take irregular critical curves into account. We devise a numerical method based on the Metropolis-Hastings algorithm: an elliptical generalization of the NFW density profile is used to fit a lens model to an observed configuration of giant luminous arcs while simultaneously optimizing the geometry. A semi-analytic method, which derives geometric parameters from critical points, is discussed as a faster alternative. We test the approaches on mock observations of gravitational lensing by a numerically simulated cluster. We find that no constraints can be derived from observations of individual clusters if no knowledge of the underlying mass distribution is assumed. Uncertainties are improved if a fixed lens model is used for a purely geometrical optimization, but the choice of a parametric model may produce strong biases.

Cosmological constraints from the double source plane lens SDSSJ0946+1006

“…In Collett et al (2012) we showed that double source plane lenses (DSPLs) can be a useful, complementary cosmological probe, allowing the dark energy equation of state to be constrained independently of the Hubble constant. Jullo et al (2010) constrained cosmological parameters using 12 multiply-lensed sources behind the cluster Abell 1689, but the sparsity of lensed images and the clumpy mass distribution in clusters makes the measurement difficult; the systematic uncertainties are likely to be large (Zieser & Bartelmann 2012) and much of the information provided by the multiple background sources may need to be used to infer the complexity of the lensing mass distribution. Galaxy-galaxy strong lenses, on the other hand, tend to be very well fitted with simple mass distributions (e.g., Vegetti et al, submitted) and therefore may be preferable objects for testing cosmology.…”