Simple model of large scale structure formation

We explore constraints on inflationary models employing data on large scale structure mainly from Cosmic Background Explorer (COBE) temperature anisotropies and Infrared Asronomy Satellite (IRAS) selected galaxy surveys, taking care not to apply linear perturbation theory to data in the nonlinear regime. In models where the tensor contribution to the COBE signal is negligible, we find the spectral index of density fluctuations $n$ must exceed 0.82. Furthermore, in inflation models which generate tensor fluctuations, these must contribute less than 20% of the signal seen by COBE. The data favor cold plus hot dark matter models with $n$ close to unity and ${\Omega }_{\mathrm{HDM}}\sim 0.20-0.35$. We present realistic grand unified theories, including supersymmetric versions, which produce inflation with these properties.