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. We show that to a great extent, the CMB anisotropies depend only on the geometry of the Universe, which in a matter dominated universe is determined by $\Omega$, and the optical depth to the surface of last scattering. In particular, the location of the primary Doppler peak depends primarily on $\Omega$ and is fairly insensitive to the other unknown parameters, such as $\Omega_b$, $h$, $\Lambda$, and the shape of the power spectrum. Therefore, measurements of CMB anisotropies on small scales may be used to determine $\Omega$.