Primordial perturbations in the density of radiation and matter can be related to vacuum fluctuations of scalar fields during inflation in the very early universe. In the standard inflaton scenario this inevitably leads to a Gaussian distribution of adiabatic density perturbations, but alternative models such as the curvaton scenario or inhomogeneous reheating can yield non‐Gaussian or non‐adiabatic signatures. © 2004 American Institute of Physics