Cosmic shear with next generation redshift surveys as a cosmological probe

The expansion of the Universe causes spacetime curvature, distinguishing between distances measured along and transverse to the line of sight. The ratio of these distances, e.g., the cosmic shear distortion of a sphere defined by observations of large scale structure as suggested by Alcock and Paczyński, provides a method for exploring the expansion as a function of redshift. The theoretical sensitivity to cosmological parameters, including the dark energy equation of state, is presented. Remarkably, sensitivity to the time variation of the dark energy equation of state is best achieved by observations at redshifts $z\lesssim 1.$ While systematic errors greatly degrade the theoretical sensitivity, this probe may still offer useful parameter estimation, especially in complementarity with a distance measure such as the type Ia supernova method implemented by SNAP. Possible future observations of the Alcock-Paczyński distortion by the KAOS project on an 8-meter ground-based telescope are considered.