Effect of Background Evolution on the Curvaton Non-Gaussianity

We investigate how the background evolution affects the curvature perturbations generated by the curvaton, assuming a curvaton potential that may deviate slightly from the quadratic one, and parameterizing the background fluid density as \rho\propto a^{-\alpha}, where a is the scale factor, and \alpha depends on the background fluid. It turns out that the more there is deviation from the quadratic case, the more pronounced is the dependence of the curvature perturbation on \alpha. We also show that the background can have a significant effect on the nonlinearity parameters f_NL and g_NL. As an example, if at the onset of the curvaton oscillation there is a dimension 6 contribution to the potential at 5 % level and the energy fraction of the curvaton to the total one at the time of its decay is at 1 %, we find variations \Delta f_NL \sim \mathcal{O}(10) and \Delta g_NL \sim \mathcal{O}(10^4) between matter and radiation dominated backgrounds. Moreover, we demonstrate that there is a relation between f_NL and g_NL that can be used to probe the form of the curvaton potential and the equation of state of the background fluid.