Quantifying the 'naturalness' of the curvaton model

We investigate the probability of obtaining an observable curvature perturbation, using as an example the minimal curvaton-higgs (MCH) model. We determine 'probably observable' and 'probably excluded' regions of parameter space assuming generic initial conditions and applying a stochastic approach for the curvaton's evolution during inflation. Inflation is assumed to last longer than the N_{obs} = 55 observable e-folds, and the total number of e-folds of inflation determines the particular ranges of parameters that are probable. For the MCH model, these 'probably observable' regions always lie within the range 8 x 10^4 GeV < m_\sigma\ < 2 x 10^7 GeV, where m_\sigma\ is the curvaton mass, and the Hubble scale at horizon exit is chosen as H_* = 10^{10} GeV. Because the 'probably observable' region depends on the total duration of inflation, information on parameters in the Lagrangian from particle physics and from precision CMB observables can therefore provide information about the total duration of inflation, not just the last N_{obs} e-folds. This method could also be applied to any model that contains additional scalar fields to determine the probability that these scalar fields contribute to the curvature perturbation.