Small-scale cosmic microwave background anisotropies as a probe of the geometry of the universe

We perform detailed calculations of cosmic microwave background (CMB) anisotropies in a CDM-dominated open universe with primordial adiabatic density perturbations for a variety of reionization histories. The CMB anisotropies depend primarily on the geometry of the universe, which in a matter-dominated universe is determined by Ω, and the optical depth to the surface of last scattering. In particular, the location of the primary Doppler peak depends primarily on Ω and is fairly insensitive to the other unknown parameters, such as Ω_b, h, A, and the shape of the power spectrum. Therefore, if the primordial density perturbations are adiabatic, measurements of CMB anisotropies on small scales may be used to determine Ω.