Strong gravitational lensing statistics as a test of cosmogonic scenarios

Gravitational lensing statistics can provide a direct and powerful test of cosmic structure formation theories. Since lensing tests, directly, the magnitude of the nonlinear mass density fluctuations on lines of sight to distant objects, no issues of "bias" (of mass fluctuations with respect to galaxy density fluctuations) exist here, although lensing observations provide their own ambiguities of interpretation. We develop numerical techniques for generating model density distributions with the very large spatial dynamic range required by lensing considerations and for identifying regions of the simulations capable of multiple image lensing in a conservative and computationally efficient way that should be accurate for splittings significantly larger than 3″. Applying these techniques to existing standard Cold dark matter (CDM) (Ω = 1) and Primeval Baryon Isocurvature (PBI) (Ω = 0.2) simulations (normalized to the COBE amplitude), we find that the CDM model predicts large splitting (>8″) lensing events roughly an order-of-magnitude more frequently than the PBI model. Under the reasonable but idealized assumption that lensing structures can be modeled as singular isothermal spheres (SIS), the predictions can be directly compared to observations of lensing events in quasar samples. Several large splitting (Δθ > 8″) cases are predicted in the standard CDM model (the exact number being dependent on the treatment of amplification bias), whereas none is observed. In a formal sense, the comparison excludes the CDM model at high confidence (essentially for the same reason that CDM predicts excessive small-scale cosmic velocity dispersions.) A very rough assessment of low-density but flat CDM model (Ω = 0.3, Λ/3H²₀ = 0.7) indicates a far lower and probably acceptable level of lensing. The PBI model is consistent with, but not strongly tested by, the available lensing data, and other open models would presumably do as well as PBI. These preliminary conclusions and the assumptions on which they are based can be tested and the analysis can be applied to other cosmogonic models by straightforward extension of the work presented here.