Microwave Background Anisotropy in Low-Ω0Inflationary Models and the Scale of Homogeneity in the Universe

We study the microwave background anisotropy due to superhorizon-size perturbations in open universes with negative spatial curvature. Using results on the low-order temperature multipole moments from the Cosmic Background Explorer satellite, we find that if the homogeneity of the observable Universe arises from an early epoch of inflation, the present density parameter cannot differ from unity by more than the observed quadrupole anisotropy, $|1-{\Omega }_0|\lesssim Q\simeq 5\times {10}^{-6\mathrm{}}$, assuming preinflationary density perturbations to be of order unity. With this assumption, inflation models with low ${\Omega }_0$ either do not fit the microwave background observations or they do not solve the horizon problem.