In this thesis, I present several astrophysical applications of Galactic and cosmological microlensing.
The first few topics are on searching and characterizing extrasolar planets by means of high-magnification microlensing events. The detection efficiency analysis of Amax ~ 3000 event OGLE-2004-BLG-343 is presented. Due to human error, intensive monitoring did not begin until 43 minutes after peak, at which point the magnification had fallen to Amax ~ 1200. It is shown that, had a similar event been well sampled over the peak, it would have been sensitive to almost all Neptune-mass planets over a factor of 5 in projected separation and even would have had some sensitivity to Earth-mass planets. New algorithms optimized for fast evaluation of binary-lens models with finite-sources effects have been developed. These algorithms have enabled efficient and thorough parameter-space searches in modeling planetary high-magnification events. The detection of the cool, Jovian-mass planet MOA-2007-BLG-400Lb, discovered from an Amax = 628 event with severe finite source effects, is reported. Detailed analysis yields a fairly precise planet/star mass ratio of q = (2.5 ± 0.4) x 10-3, while the planet/star projected separation is subject to a strong close/wide degeneracy. Photometric and astrometric measurements from Hubble Space Telescope, as well as constraints from higher order effects extracted from the ground-based light curve (microlens parallax, planetary orbital motion and finite-source effects) are used to constrain the nature of planetary event OGLE-2005-BLG-071Lb. Our primary analysis leads to the conclusion that the host is an M = 0.46 ± 0.04 MSun M dwarf and that the planet has mass Mp = (3.8 ± 0.4) MJupiter, which is likely to be the most massive planet yet discovered that is hosted by an M dwarf.
Next a spaced-based microlens parallax is determined for the first time using Spitzer and ground-based observations for binary-lens event OGLE-2005-SMC-001. The parallax measurement yields a projected velocity about 239 km/s, the typical value expected for halo lenses, but an order of magnitude smaller than would be expected for lenses lying in the Small Magellanic Cloud (SMC) itself.
Finally, I propose using quasar microlensing to probe Mg II and other
absorption "cloudlets" with sizes ~ 10-4.0 - 10-2.0 pc in the intergalactic medium. I show that significant spectral variability on timescales of months to years can be induced by such small-scale absorption "cloudlets" toward a microlensed quasar. With numerical simulations, I demonstrate the feasibility of applying this method to Q2237+0305, and I show that high-resolution spectra of this quasar in the near future would provide a clear test of the existence of such metal-line absorbing "cloudlets".