Observational constraints on the curvaton model of inflation

Simple curvaton models can generate a mixture of correlated primordial adiabatic and isocurvature perturbations. The baryon and cold dark matter isocurvature modes differ only by an observationally null mode in which the two perturbations almost exactly compensate, and therefore have proportional effects at linear order. We discuss the cosmic microwave background (CMB) anisotropy in general mixed models, and give a simple approximate analytic result for the large scale CMB anisotropy. Working numerically we use the latest Wilkinson Microwave Anisotropy Probe (WMAP) observations and a variety of other data to constrain the curvaton model. We find that models with an isocurvature contribution are not favored relative to simple purely adiabatic models. However a significant primordial totally correlated baryon isocurvature perturbation is not ruled out. Certain classes of curvaton model are thereby ruled out; other classes predict enough non-Gaussianity to be detectable by the Planck satellite. In the Appendixes we review the relevant equations in the covariant formulation and give series solutions for the radiation dominated era.