Cold dark matter models with a cosmological constant

We use linear and quasi-linear perturbation theory to analyse cold dark matter models of structure formation in spatially flat models with a cosmological constant. Both a tilted spectrum of density perturbations and a significant gravitational wave contribution to the microwave anisotropy are allowed as possibilities. We provide normalizations of the models to microwave anisotropies, as given by the four-year {\it COBE} observations, and show how all the normalization information for such models, including tilt, can be condensed into a single fitting function which is independent of the value of the Hubble parameter. We then discuss a wide variety of other types of observations. We find that a very wide parameter space is available for these models, provided $\Omega_0$ is greater than about 0.3, and that large-scale structure observations show no preference for any particular value of $\Omega_0$ in the range 0.3 to 1.