Gravitational instability theories usually assume that the spectrum of primordial density fluctuations follows a power law with amplitudes drawn from a Gaussian distribution, and the existence of some form of dark matter. Alternative theories depend upon topological defects, such as monopoles, cosmic strings, textures, or other dynamical effects to generate present day structures. Various theories predict different angular spectra for CMB fluctuations. Topological defect models generally predict non-Gaussian statistics for the fluctuation amplitude distribution. We will develop methodology and software to find confidence intervals for moments of the CMB temperature distribution, multipole coefficients, and spectral parameters of ``power laws'' predicted by some theories. These estimates also test the gaussianity of the initial fluctuations. Our new methodology will include minimax estimation and ``strict bounds,'' and will rely heavily on large-scale nonlinear optimization. We will employ a network of 35 Sun SPARCStations to perform distributed simulations and solve large optimization problems in parallel. Both the minimax and strict bounds approaches require a priori constraints on the CMB, which we will derive from physical theory and by incorporating the results from other experiments on different spatial scales. The Cosmic Background Explorer (COBE) team recently announced the detection of fluctuations in the temperature of the Cosmic Microwave Background (CMB). CMB fluctuations trace the primordial variations in the density of matter and energy as they were about 300,000 years after the Big Bang. These density variations are required by cosmological theories to account for observed present-day large-scale structure, e.g., galaxies, clusters of galaxies, superclusters and voids. Different theories require different structure in the primordial density, and a principal goal is to use COBE data to discriminate among these theories. The statistical tools currently used in the astrophysics comm unity do not permit rigorous discrimination among these theories: the tools are subject to known biases whose magnitudes are largely unknown. We will develop and apply new tools that use constraints derived from the cosmological theories and from other experiments to limit the possible bias and reduce the uncertainty.
