Generation of Isocurvature from Curvature Inhomogeneities on Super-Horizon Scales

Here it is shown 1) how isocurvature inhomogeneities correlated on causally disconnected (super-horizon) scales are generated from curvature inhomogeneities which are known to be correlated on these scales 2) that super-horizon isocurvature generation is nearly inevitable for non-equilibrium chemical processes 3) that the amplitude of the compositional isocurvature correlations a) can be large for production of rare objects, b) falls off rapidly with separation c) falls off at scales below the horizon when these modes are generated. These two fall-offs results in an "isocurvature bump" in the power spectrum. Isocurvature generation is illustrated by the process of dark matter freeze-in, computed here with both separate universe modelling and linear perturbation theory. For freeze-in the most prominent isocurvature modes are inhomogeneities in the ratio of dark matter to standard model matter. Much smaller inhomogeneities in the ratio of baryons to standard model entropy are also produced. Previous constraints on freeze-in from Ly-$\alpha$ clouds limit the bump enhancement to $\lesssim10\%$ on comoving scales $\lesssim1\,$Mpc. Current observations are not sensitive to the isocurvature modes generated in viable freeze-in models. Results are obtained using a somewhat novel framework to describe cosmological inhomogeneities.