PURSUING PARAMETERS FOR CRITICAL-DENSITY DARK-MATTER MODELS

We present an extensive comparison of models of structure formation wi th observations, based on linear and quasi-linear theory. We assume a critical matter density, and study both cold dark matter models and co ld plus hot dark matter models. We explore a wide range of parameters, by varying the fraction of hot dark matter Omega(v), the Hubble param eter h and the spectral index of density perturbations n, and allowing for the possibility of gravitational waves from inflation influencing large-angle microwave background anisotropies. New calculations are m ade of the transfer functions describing the linear power spectrum, wi th special emphasis on improving the accuracy on short scales where th ere are strong constraints. For assessing early object formation, the transfer functions are explicitly evaluated at the appropriate redshif t. The observations considered are the four-year COBE observations of microwave background anisotropies, peculiar velocity flows, the galaxy correlation function, and the abundances of galaxy clusters, quasars and damped Lyman alpha systems. Each observation is interpreted in ter ms of the power spectrum filtered by a top-hat window function. We fin d that there remains a viable region of parameter space for critical-d ensity models when all the dark matter is cold, though h must be less than 0.5 before any fit is found and n significantly below unity is pr eferred. Once a hot dark matter component is invoked, a wide parameter space is acceptable, including n similar or equal to 1. The allowed r egion is characterized by Omega(v) less than or similar to 0.35 and 0. 60 less than or similar to n less than or similar to 1.25, at 95 per c ent confidence on at least one piece of data. There is no useful lower bound on h, and for curious combinations of the other parameters it i s possible to fit the data with h as high as 0.65.