Cosmic shear and power spectrum normalization with the Hubble Space Telescope

Weak lensing by large-scale structure provides a direct measurement of matter fluctuations in the universe. We report a measurement of this "cosmic shear" based on 271 Wide Field Planetary Camera 2 archival images from the Hubble Space Telescope Medium Deep Survey. Our measurement method and treatment of systematic effects were discussed in an earlier paper. We measure the shear variance on scales ranging from 0.'7 to 1.'4, with a detection significance greater than 3.8 sigma. This allows us to measure the normalization of the matter power spectrum to be sigma(8) = (0.94 +/- 0.10 +/- 0.14)(0.3/Omega(m))(0.44) (0.21/Gamma)(0.15), in a LambdaCDM universe. The first 1 sigma error includes statistical errors only, while the latter also includes (Gaussian) cosmic variance and the uncertainty in the galaxy redshift distribution. Our results are consistent with earlier cosmic shear measurements from the ground and from space. We compare our cosmic shear results and those from other groups to the normalization from cluster abundance and galaxy surveys. We find that the combination of four recent cosmic shear measurements are somewhat inconsistent with the recent normalization using these methods and discuss possible explanations for the discrepancy.