Cosmological constant, COBE cosmic microwave background anisotropy, and large-scale clustering

A flat, scale-free, low-density cold dark matter model with a positive cosmological constant is one of the surviving scenarios after the COBE discovery of large-scale anisotropy in the cosmic background radiation. We calculate the expected properties of the model when normalized to the anisotropy measured by COBE, for various large-scale structure observations: the CfA and IRAS galaxy power spectra, the galaxy peculiar velocities, the bulk-flow motion, the APM galaxy angular correlation function, and the cluster mass function. Several effects due to the cosmological constant and properties of primordial fluctuations from inflation are taken into account. We find that a flat model (Ω + Ω_Λ = 1) with Ωh ≈ 0.25-0.3 is consistent with all the above large-scale structure observations. A value of Ω ≳ 0.3-0.4 is also consistent with the observed age of the globular clusters and a galaxy bias of b ∼ 1.5. The streaming velocity test fits the data at the 1.6 σ level and appears to be a critical test for the model.