4.2 Gravitational lensing

Observations of gravitational lenses [143] provide measures of the abundance and strength of nonlinear potential fluctuations along the lines of sight to distant objects. Since these calculations are sensitive to the gravitational potential, they may be more reliable than galaxy and velocity field measurements as they are not subject to the same ambiguities associated with biasing effects. Also, because different cosmological models predict different mass distributions, especially at the higher redshifts, lensing calculations can potentially be used to confirm or discard competing cosmological models.

As an alternative to solving the computationally demanding lens equations, Cen et al. [55] developed an efficient scheme to identify regions with surface densities capable of generating multiple images accurately for splittings larger than three arcseconds. They applied this technique to a standard CDM model with Ω0 = 1, and found that this model predicts more large angle splittings (> 8′′) than are known to exist in the observed Universe. Their results suggest that the standard CDM model should be excluded as a viable model of our Universe. A similar analysis for a flat low density CDM model with a cosmological constant (Ω0 = 0.3, 2 Λ ∕(3H 0) = 0.7) suggests a lower and perhaps acceptable number of lensing events. However, an uncertainty in their studies is the nature of the lenses at and below the resolution of the numerical grid. They model the lensing structures as simplified Singular Isothermal Spheres (SIS) with no distinctive cores.

Large angle splittings are generally attributed to larger structures such as clusters of galaxies, and there are indications that clusters have small but finite core radii rcore ∼ 20– 30h −1 kpc. Core radii of this size can have an important effect on the probability of multiple imaging. Flores and Primack [74] considered the effects of assuming two different kinds of splitting sources: isothermal spheres with small but finite core radii and radial density profiles 2 2 − 1 ρ ∝ (r + rcore), and spheres with a Hernquist density profile −1 − 3 ρ ∝ r (r + a ), where −1 rcore ∼ 20– 30h kpc and −1 a ∼ 300h kpc. They find that the computed frequency of large-angle splittings, when using the nonsingular profiles, can potentially decrease by more than an order of magnitude relative to the SIS case and can bring the standard CDM model into better agreement with observations. They stress that lensing events are sensitive to both the cosmological model (essentially the number density of lenses) and to the inner lens structure, making it difficult to probe the models until the structure of the lenses, both observationally and numerically, is better known.

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