The linearly perturbed sky

The appearance of the sky in a Friedmann universe perturbed by linear density inhomogeneities is analysed. Particular attention is given to gravitational lensing of microwave background anisotropies. We derive the rms absolute and relative deflections of light rays as a function of redshift and angular separation. For cold dark matter perturbations we find rms deflections ∼ 4 arcmin, coherent for beam widths < 3 arcmin. This implies possible enhancement of anisotropies by a factor ∼ 2 and an apparent axial ratio of distant spherical sources of ∼ 3, increasing the difficulty of observing objects beyond z ≅ 4. (author)