Gravitational lensing by smooth inhomogeneities in the universe
Abstract
We review the formalism developed by Gunn on the gravitational lensing effect of smooth inhomogeneities in the Universe and derive some new simple analytical expressions for the dispersion in amplification. Two models for the distribution and evolution of density fluctuations are considered, namely a universe dominated by cold dark matter (CDM), and a scalefree universe with an initial density fluctuation spectrum corresponding to white noise. We find that the dispersion in amplification due to largescale (> 0.5 h^1^ Mpc) structures is negligible in both models even for sources at redshifts z_s ~ 4, but the dispersion increases substantially when matter distribution on smaller scales is taken into consideration and it is very sensitive to the nature of the mass distribution. In the CDM model, the dispersion remains small for z_s_ <~ 4 even for a smoothing scale as small as 10 h^1^ kpc. In the scalefree model, the dispersion is about 33 per cent for z_s_ ~ 2.5 if the smoothing scale is 30 h^1^ kpc. Such a large dispersion indicates that shear may be appreciable along some linesofsight, resulting in appreciable image distortions and enhanced amplification. Lensing effects have important implications for attempts to determine the luminosity function of highredshift objects such as quasars. The efficacy increases with the redshift of the source and the resulting redshiftdependent changes in the luminosity function could easily be mistaken for evolution. Until we understand better the distribution and evolution of smallscale density inhomogeneities and their effects, we should be cautious about interpreting the observed luminosity function of highredshift objects. On the other hand, if there are observable standard candles at z_s_ >~ 2, they can be used to test models for the distribution and evolution of inhomogeneities in the Universe.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 1991
 DOI:
 10.1093/mnras/250.2.407
 Bibcode:
 1991MNRAS.250..407B
 Keywords:

 Dark Matter;
 Gravitational Lenses;
 Red Shift;
 Universe;
 Analytic Functions;
 Astronomical Models;
 Formalism;
 Inhomogeneity;
 Mass Distribution;
 Astrophysics