Microwave background anisotropy induced by gravitational waves

A cosmological background of gravitational waves induces redshift perturbations in light transversing it. Calculations of this Sachs-Wolfe effect on the microwave background are presented in an Omega = 1 Friedmann universe as a function of angular scale and gravitational wave spectrum. Blurriness of the last-scattering surface can cause nonnegligible dilution of the anisotropy for wavelengths less than about 100 Mpc. The limit implied for the energy density of the gravitational waves is given. A difficulty in associating a linear scale with an angular anisotropy, due to the clumpiness of the universe, is also pointed out.