A Simple Model of Large Scale Structure Formation

We explore constraints on inflationary models employing data on large scale structure mainly from COBE temperature anisotropies and IRAS selected galaxy surveys, taking care not to apply linear perturbation theory to data in the non-linear regime. In models where the tensor contribution to the COBE signal is negligible, we find the spectral index of density fluctuations $n$ must exceed 0.7. Furthermore the COBE signal cannot be dominated by the tensor component, implying $n>0.85$ in such models. The data favors cold plus hot dark matter models with $n$ close to unity and ${\mathrm{\Omega }}_{HDM}\sim 0.20-0.35$. We present realistic grand unified theories, including supersymmetric versions, which produce inflation with these properties.