Visions of gravitation: Topics in gravitational lensing

I present theoretical work on gravitational lensing and its use in constraining the structure of our galaxy, other galaxies and the universe as a whole. I begin with the effects of a galactic bar on the spatial and timescale distributions of microlensing events in the galactic center. Then the statistics of microlensing events in the Large Magellanic Cloud are calculated under the assumption that the Milky Way's dark halo is made of MACHOs clumped into clusters. I find that the constraints on the fraction of mass in MACHOs is significantly relaxed if the cluster masses and sizes are similar to those of globular clusters. Such clusters are detectable as spikes in the timescale distribution of events.; The average distance-redshift relation in an inhomogeneous universe is considered with the conclusion that it need not precisely agree with the relation in a homogeneous universe. Averages over the sky and averages over sources will necessarily give different, but related, values for the distance. Lensing by multiple lenses and large scale structure is treated and applied to the cosmic microwave background (CMB). I show that the average magnification of an equal redshift surface is positive, but small in standard models, and that lensing both smoothes out the CMB power spectrum and decreases the slope of its damping tail by transferring power from larger to smaller scales. The latter effect becomes increasingly important beyond ℓ ∼ 1800. After lensing, the CMB power spectrum will no longer be a degenerate function of cosmological parameters Oo and O Λ.; I then show that the weak gravitational lensing of high redshift type Ia supernovae has the potential to probing the distribution and composition of dark matter. The statistics of this lensing strongly discriminates between dark matter (DM) made of macroscopic compact objects and DM made of microscopic elementary particles. With current noise levels, ∼50--100 supernovae at redshifts ∼1 can clearly distinguish between these DM candidates. It is further shown that if dark matter is composed of microscopic particles correlations in SN luminosities and foreground galaxy properties can be used to detect lensing and constrain the size and mass of galaxy halos.