Scale-dependent non-Gaussianity and the CMB Power Asymmetry

We introduce an alternative parametrisation for the scale dependence of the non-linearity parameter $f_{\mathrm{N}\mathrm{L}}$ in quasi-local models of non-Gaussianity. Our parametrisation remains valid when $f_{\mathrm{N}\mathrm{L}}$ changes sign, unlike the commonly adopted power law ansatz $f_{\mathrm{N}\mathrm{L}}(k)\propto k^{n_{f_{\mathrm{N}\mathrm{L}}}}$. We motivate our alternative parametrisation by appealing to the self-interacting curvaton scenario, and as an application, we apply it to the CMB power asymmetry. Explaining the power asymmetry requires a strongly scale dependent non-Gaussianity. We show that regimes of model parameter space where $f_{\mathrm{N}\mathrm{L}}$ is strongly scale dependent are typically associated with a large $g_{\mathrm{N}\mathrm{L}}$ and quadrupolar power asymmetry, which can be ruled out by existing observational constraints.