  We study the functional dependence of the spin-weighted angular moments of
the two-point correlation function of the three dimensional cosmic shear on the
expansion history of the universe. We first express the redshift dependent
total equation of state parameter in terms of the growing mode of the gauge
invariant metric perturbation in the conformal-Newtonian gauge for the case of
adiabatic perturbations. We then express the redshift dependent angular moments
of the shear two-point correlation function as an integral in terms of the
metric perturbation. We present the final explicit expression for the case of a
Harrison-Zeldovich spectrum of primordial perturbations. Our analysis is
restricted to the linear regime. We use our results to make a preliminary study
of the required sensitivity that will allow cosmic shear observations to add
significant information about the expansion history of the universe.
