Lensing effects in an inhomogeneous universe

TL;DR

This paper extends a gravitational lensing method to include multiple matter types and realistic dark matter halos, analyzing their effects on supernova luminosity measurements in an inhomogeneous universe.

Contribution

The authors generalize Holz & Wald's lensing method to incorporate multiple fluids with pressure and realistic NFW dark matter halos, providing analytical formulas for lensing probabilities.

Findings

Large supernova samples can reveal dark matter halo features

Lensing effects are similar for isothermal and NFW models when normalized

Analytical fitting formulas for lensing probabilities are provided

Abstract

Recently, Holz & Wald have presented a new method for determining gravitational lensing effects on, e.g., supernova luminosity versus redshift measurements in inhomogeneous universes. In this paper, their method is generalized in several ways: First, the matter content is allowed to consist of several different types of fluids, possibly with non-vanishing pressure. Second, besides lensing by simple point masses and singular isothermal spheres, the more realistic halo dark matter distribution proposed by Navarro, Frenk & White (NFW), based on N-body simulation results, is treated. We discuss various aspects of the accuracy of the method, such as luminosity corrections, and statistics, for multiple images. We find in agreement with other recent work that a large sample of supernovae at large redshift could be used to extract gross features of the mass distribution of the lensing dark matter halos, such as the existence of a large number of point-like objects. The results for the isothermal sphere and the NFW model are, however, very similar if normalized to the observed luminosity distribution of galaxies. We give convenient analytical fitting formulas for our computed lensing probabilites as a function of magnification, for several redshifts.