Observational Tests of One-Bubble Open Inflationary Cosmological Models

Motivated by recent studies of the one-bubble inflationary scenario, simple open cold dark matter models are tested for consistency with cosmological observations. The initial perturbation spectrum is derived by solving for the evolution of fluctuations in an open inflationary stage. A likelihood analysis is performed for the Cosmic Microwave Background anisotropies using the two-year COBE DMR data and considering models based on both the Bunch-Davies and conformal vacua. Having normalized the perturbation spectrum to fit the COBE data, we reconsider the validity of the open model from the view point of cosmic structure formation. Open models may be severely constrained by the COBE likelihood analysis. In particular, small values of $\Omega_0$ are ruled out in the Bunch-Davies case: we find that $\Omega_0\ge 0.34$ at 95\% confidence for this model.