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A0 over dP affine parameter amount of lensing angle of observation angular scale arcminutes average change bending angle change in angular change in separation CMB photons core radius cosmic microwave background decreases define density profile dimensionless distance effect of gravitational encountered evolved mass spectra expect the evolved Figure galaxy formation given mass graph gravitational lensing gravitational potential Hubble constant impact parameter increasing initial density perturbations intrinsic fluctuations isothermal sphere Kashlinsky 1987 km sec-1 Mpc-1 last scattering surface lens equation lens plane lensers lensing effect lensing may alter linear separation mass distribution mass profiles mass scale mass spectrum normalization number density observed angular separation observer/lens line pair of photons photons starting photons travel plots point mass lenses present Press and Schecter r.m.s. shift reionization solid line source plane starting at b0 total radius trajectory travel from z(CMB unevolved mass unevolved models University of Virginia z)dM zero