Optimal transport provides an efficient method to infer the displacement of objects by mapping their initial positions to their present-day locations over cosmic time; equivalently, it enables the reconstruction of initial positions from measurements taken at later times. The method has been shown to be accurate even if positions for only a biased subset of the particles are measured, provided that the initial displacement field was Gaussian. The method does not rely on the assumption of a Gaussian displacement field and thus may be extended to the reconstruction of non-Gaussian initial conditions. Here, we demonstrate how this is achieved for a class of “local” primordial non-Gaussian fields of current interest in cosmology. For these models, there is a distinctive signature in the large scale clustering of biased tracers that depends on the product of the primordial amplitude $f_{\mathrm{NL}}$ and the nature of the tracers $b_{\varphi }$. Our method exploits the fact that this signature is not present in the full field; it is only present in biased fields. Therefore, the mass that is not in the biased subset, what we call the “dust,” also has a characteristic scale dependence, albeit of a different amplitude. We show that the quality of the optimal transport reconstruction improves as the model for this dust becomes more realistic. Importantly, the dust model requires only the combination $f_{\mathrm{NL}}{b}_{\varphi }$, and not $f_{\mathrm{NL}}$ itself: this is the same quantity that the scale-dependent bias signal measures directly, so the reconstruction is conditioned on an observable rather than on prior knowledge of the primordial amplitude.

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• Cosmology