Perturbation amplitude in isocurvature inflation scenarios

Abstract

We make a detailed calculation of the amplitude of isocurvature perturbations arising from inflationary models in which the cold dark matter is represented by a scalar field which acquires perturbations during inflation. We use this to compute the normalization to large-angle microwave background anisotropies. Unlike the case of adiabatic perturbations, the normalization to COBE fixes the spectral index of the perturbations; if adiabatic perturbations are negligible then $n_{iso} \simeq 0.4$. Such blue spectra are also favoured by other observational data. Although the pure isocurvature models are unlikely to adequately fit the entire observational data set, these results also have implications for models with mixed adiabatic and isocurvature perturbations.