Why not consider closed universes?

We consider structure formation and cosmic microwave background (CMB) anisotropies in a closed universe, both with and without a cosmological constant. The CMB angular power spectrum and the matter transfer function are presented, along with a discussion of their relative normalization. This represents the first full numerical evolution of density perturbations and anisotropies in a spherical geometry. We extend the likelihood function versus Omega from the COBE 2 year data to Omega greater than or equal to 1. For large Omega the presence of a very steep rise in the spectrum toward low l allows us to put an upper limit of Omega greater than or equal to 1.5 (95% CL) for primordial spectra with n less than or equal to 1. This compares favorably with existing Emits on Omega. We show that there are a range of closed models that are consistent with observational constraints while being even older than the currently popular flat models with a cosmological constant. Future constraints from degree scale CMB data may soon probe this region of parameter space. A derivation of the perturbed Einstein, fluid, and Boltzmann equations for open and closed geometries is presented in an Appendix.