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Resolving primordial physics through correlated signatures

We discuss correlations among spectral observables as a new tool for differentiating between models for the primordial perturbation. We show that if generated in the isocurvature sector, a running of the scalar spectral index is correlated with the statistical properties of non-Gaussianities. In particular, we find a large running will inevitably be accompanied by a large running of $f_{\rm NL}$ and enhanced $g_{\rm NL}$, with $g_{\rm NL}\gg f_{\rm NL}^2$. If the tensor to scalar ratio is large, a large negative running must turn positive on smaller scales. Interestingly, the characteristic scale of the transition could potentially distinguish between the inflaton and isocurvature fields.