Secondary gravitational anisotropies in open universes

The applicability of the potential approximation in the case of open universes is tested. Great Attractor‐like structures are considered in the test. Previous estimates of the cosmic microwave background anisotropies produced by these structures are analysed and interpreted. The anisotropies corresponding to inhomogeneous ellipsoidal models are also computed. It is proved that, whatever the spatial symmetry may be, Great Attractor‐like objects with extended cores (radii ∼10 h −1 ), located at redshift z =5.9 in an open universe with density parameter Ω 0 =0.2, produce secondary gravitational anisotropies of the order of 10 −5 on angular scales of a few degrees. The amplitudes and angular scales of the estimated anisotropy decrease as the Great Attractor size decreases. For comparable normalizations and compensations, the anisotropy produced by spherical realizations is found to be smaller than that of ellipsoidal models. This anisotropy appears to be an integrated effect along the photon geodesics. Its angular scale is much greater than that subtended by the Great Attractor itself. This is easily understood by taking into account the fact that the integrated effect is produced by the variations of the gravitational potential, which seem to be important in large regions subtending angular scales of several degrees. As a result of the large size of these regions, the spatial curvature of the universe becomes important and, consequently, significant errors (∼30 per cent) arise in estimates based on the potential approximation. As is emphasized in this paper, two facts should be taken into account carefully in some numerical estimates of secondary gravitational anisotropies in open universes: (1) the importance of scales much greater than those subtended by the cosmological structures themselves, and (2) the compatibility of the potential approximation with the largest scales.