Inflation and mixed dark matter models

Recent observations of large-scale structure, including those by COBE, have prompted many authors to discuss modifications of the standard cold dark matter model. Two of these, a tilted spectrum and a gravitational wave contribution to the COBE signal, are at some level demanded by theory under the usual assumption that inflation generates the primeval perturbations. A third modification, the motivation for which comes by contrast from observation, is the introduction of a component of hot dark matter, to give the mixed dark matter model. We discuss the implications of taking these modifications together, and compare with a range of observational data including microwave anisotropies, bulk flows and cluster and quasar abundances. Models without a hot component fare badly, while those with such a component, either with or without mild inflationary corrections, can explain the data, although marginally. If a hot dark matter component is the mechanism of choice to explain the data, very strong constraints on inflationary models will ensue.