Microwave background anisotropy in low-$\Omega_0$ inflationary models and the scale of homogeneity in the Universe

Abstract

We study the microwave background anisotropy due to superhorizon-size perturbations (the Grischuk-Zel'dovich effect) in open universes with negative spatial curvature. Using COBE results on the low-order temperature multipole moments, 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, $|1-\Omega_0| \alt Q \simeq 5\times 10^{-6}$. Thus, inflation models with low $\Omega_0$ either do not fit the microwave background observations or they do not solve the horizon problem.