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Here it is shown 1) how isocurvature inhomogeneities correlated on causallydisconnected (super-horizon) scales are generated from curvatureinhomogeneities which are known to be correlated on these scales 2) thatsuper-horizon isocurvature generation is nearly inevitable for non-equilibriumchemical processes 3) that the amplitude of the compositional isocurvaturecorrelations a) can be large for production of rare objects, b) falls offrapidly with separation c) falls off at scales below the horizon when thesemodes are generated. These two fall-offs results in an "isocurvature bump" inthe power spectrum. Isocurvature generation is illustrated by the process ofdark matter freeze-in, computed here with both separate universe modelling andlinear perturbation theory. For freeze-in the most prominent isocurvature modesare inhomogeneities in the ratio of dark matter to standard model matter. Muchsmaller inhomogeneities in the ratio of baryons to standard model entropy arealso produced. Previous constraints on freeze-in from Ly-$\alpha$ clouds limitthe bump enhancement to $\lesssim10\%$ on comoving scales $\lesssim1\,$Mpc.Current observations are not sensitive to the isocurvature modes generated inviable freeze-in models. Results are obtained using a somewhat novel frameworkto describe cosmological inhomogeneities.

Generation of Isocurvature from Curvature Inhomogeneities on Super-Horizon Scales