Superhorizon Isocurvature as a Window into Dark Matter Production

TL;DR

The paper addresses how primordial isocurvature, especially from a dark radiation sector, affects the superhorizon evolution of curvature perturbations and leaves imprints on dark matter production. Using the separate-universe approach, it derives a closed framework for the evolution of perturbations in the long-wavelength limit and applies it to DM production via freeze-in and freeze-out in the presence of DR isocurvature. Analytic toy models and detailed numerical analyses show that DM inevitably acquires isocurvature correlated with DR, with a final DM isocurvature that scales linearly with the DR energy density at DM production and with the initial DR isocurvature, characterized by an order-one slope that differs between FI (negative) and FO (positive). These results imply that future CMB and LSS observations could distinguish DM production mechanisms by measuring the DM isocurvature amplitude and its correlation with DR/neutrino isocurvature, providing a new window into DM microphysics and the early-universe cosmology.

Abstract

In the presence of primordial isocurvature perturbations, for example in a separate dark radiation sector, the superhorizon evolution of curvature perturbations becomes nontrivial. If the dark sector is radiation-like and constitutes a significant fraction of the energy density, its isocurvature can imply isocurvature in the inflaton sector even without direct interactions between the sectors. In this article, we revisit superhorizon curvature and isocurvature evolution in the long-wavelength limit systematically, drawing a simple picture of how to understand the nature of these fluctuations from first principles and without brute-force cosmic perturbation theory. We show how the described setup is able to source isocurvature in simple models of dark matter such as freeze-in and freeze-out and demonstrate that future measurements of matter and neutrino isocurvature can potentially discriminate between these two mechanisms.

Figures (11)

• Figure 1: Geometric interpretation of the coordinate invariant perturbations as offsets in e-folds $\delta N$ (arrows) or equivalent time $\delta t=\delta N /H$ for spatially separated patches of the universe between slicings of constant density ($\delta \rho=0$) and the flat slicing with vanishing metric fluctuation ($\psi=0$).
• Figure 2: In the adiabatic scenario (left), the single inflaton $\phi$ reheats the universe. The time of inflaton reheating is marked by RH. All components of the cosmic fluid follow the same $\zeta$. It is inherited by the resulting DM, standard model neutrinos $\nu$ and photons $\gamma$, which are all decoupled at a later time (DEC). In the scenario of an additional decaying curvaton $\sigma$ (center), its energy density is completely transferred into the radiation sector, which is dominantly sourced by the inflaton field $\phi$. The decay of the curvaton starts after inflaton reheating, but in this case before DM decouples, resulting in purely adiabatic perturbations again. In the curvaton scenario, the inflaton carries zero $\zeta$. If we consider an additional inflationary field $\phi_2$ (right), which sources a dark sector consisting only of DR, the DM can inherit isocurvature by the presence of non-negligible DR curvature perturbations, even if DR couples only gravitationally to the other sector.
• Figure 3: Background evolution of the direct curvaton decay for two different decay rates. We show the energy density for the curvaton (purple), the radiation sector (green) and the total energy density (red). The dashed line is the same setup with a 30 percent higher initial curvaton abundance, resembling a patch with a density perturbation in the curvaton. Due to the matter scaling of the curvaton, the total energy density normalized to the radiation energy density increases. The smaller decay constant in (b) causes the curvaton to dominate the energy density before decaying to radiation.
• Figure 4: The numerical evolution of curvature and isocurvature perturbations is shown. The initial curvature of the curvaton field (purple) is normalized to unity. The radiation (green) starts with zero curvature. The isocurvature perturbation (black) is divided by 3. The total curvature perturbation is depicted as well (red). As can be seen from the background evolution in \ref{['fig:numerical_evolution_curvaton_decay_background']}, in the case of a small decay constant the matter-scaling curvaton sector can dominate the energy density before its decay, thereby leaving a stronger imprint of its associated curvature perturbations.
• Figure 5: Evolution of background energy densities and curvature perturbations in terms of e-folds for freeze-in (top, DM in red) and freeze-out (bottom, DM in purple). The color is corresponding to the fluids. In the right panels, the black dashed line is the isocurvature perturbation between the SM and the DM sector. The initial DR energy density is the same for the two presented setups. In the freeze-out, the equilibrium energy density is included as dashed purple line.