Dynamical Dark Matter: I. Theoretical Overview

TL;DR

The paper introduces dynamical dark matter (DDM), a framework in which the dark sector comprises a vast ensemble of components with a spectrum of masses, lifetimes, and abundances that balance stability against abundance, producing a time-dependent Omega_tot and a nontrivial effective equation of state w_eff. It demonstrates a concrete realization with an infinite tower of Kaluza-Klein states living in the bulk of large extra dimensions, where misalignment production and brane-bulk couplings yield inverse relations between abundances and decay widths across the tower, enabling sustained dark-matter content without requiring absolute stability. The work also highlights distinctive phenomenology—decoherence, coupling suppression for light modes, and a lack of a single DM mass or cross-section—and lays out a broad phenomenological framework and future directions, including explicit model realizations and detailed constraints in companion papers. Together, these results position dynamical dark matter as a viable, testable alternative to traditional single-component, stable dark-matter scenarios, with potential implications for string theory and extra-dimensional physics.

Abstract

In this paper, we propose a new framework for dark-matter physics. Rather than focus on one or more stable dark-matter particles, we instead consider a multi-component framework in which the dark matter of the universe comprises a vast ensemble of interacting fields with a variety of different masses, mixings, and abundances. Moreover, rather than impose stability for each field individually, we ensure the phenomenological viability of such a scenario by requiring that those states with larger masses and Standard-Model decay widths have correspondingly smaller relic abundances, and vice versa. In other words, dark-matter stability is not an absolute requirement in such a framework, but is balanced against abundance. This leads to a highly dynamical scenario in which cosmological quantities such as Omega_{CDM} experience non-trivial time-dependences beyond those associated with the expansion of the universe. Although it may seem difficult to arrange an ensemble of states which have the required decay widths and relic abundances, we present one particular example in which this balancing act occurs naturally: an infinite tower of Kaluza-Klein (KK) states living in the bulk of large extra spacetime dimensions. Remarkably, this remains true even if the stability of the KK tower itself is entirely unprotected. Thus theories with large extra dimensions --- and by extension, certain limits of string theory --- naturally give rise to dynamical dark matter. Such scenarios also generically give rise to a rich set of collider and astrophysical phenomena which transcend those usually associated with dark matter.

Figures (8)

• Figure 1: A sketch of our dynamical dark-matter scenario in which the dark matter of the universe comprises a vast ensemble of individual components with different masses, abundances, and lifetimes. This plot illustrates the evolution of the abundance of each dark-matter component as a function of time, assuming that all abundances are initially established at a common time (chosen here to be prior to or during the inflationary era), with values that decrease as a function of the component mass. For all subsequent times, these abundances scale as vacuum energy until $3H(t)=2 m_i$, after which point they scale as matter. Open circles indicate states which inflate away, while closed circles indicate states which decay into SM particles with associated lifetimes that decrease with increasing mass. In our scenario, the lifetimes and abundances are balanced against each other in such a way that there continue to exist a plethora of dark-matter states which survive at the present time: although each such state has an extremely small abundance $\Omega_i\ll 1$, they collectively reproduce $\Omega_{\rm CDM}$. Nevertheless, because of their extremely small abundances, states which have already decayed into SM particles leave negligible imprints on the CMB and other observable astrophysical and cosmological backgrounds. An important feature of this scenario is that it is fully dynamical, with the composition and properties of the dark matter continuing to experience a non-trivial time evolution before, during, and even after the current epoch.
• Figure 2: A sketch of the total dark-matter abundance in our scenario during the final, matter-dominated era. Even though each dark-matter component individually has $w=0$, the spectrum of lifetimes and abundances of these components conspire to produce a time-dependent total dark-matter abundance $\Omega_{\rm tot}$ which corresponds to an effective equation of state with $w>0$.
• Figure 3: Values of $A_\lambda$ (falling curves) and $\tilde{\lambda}^2 A_\lambda$ (rising curves), plotted as functions of the mass eigenvalues $\tilde{\lambda}/y= \lambda R$ for $y=\pi$ (black), $y=\sqrt{\pi}$ (blue), and $y=1$ (red). For each $y$, there are only a discrete set of corresponding allowed eigenvalues $\tilde{\lambda}$ (indicated with solid dots); note that the quantity $\tilde{\lambda}/y = \sqrt{\lambda^2-M^2} R$ takes values closer to ${ Z Z}+1/2$ near the bottom of each tower and shifts to values closer to ${ Z Z}$ as $\lambda$ increases. In each case, we see that $A_\lambda$ falls with increasing $\tilde{\lambda}$, while $\tilde{\lambda}^2 A_\lambda$ increases with increasing $\tilde{\lambda}$ and ultimately reaches an asymptote $\tilde{\lambda}^2 A_\lambda\to \sqrt{2}$ as $\tilde{\lambda} \to \infty$.
• Figure 4: The quantity $\sum_\lambda \tilde{\lambda}^{1/2} A_\lambda^2$, plotted as a function of $y$. Note that the total dark-matter abundance $\Omega_{\rm tot}$ prior to the onset of significant KK decays is proportional to this quantity if the individual KK abundances are initially established through a staggered turn-on during the radiation-dominated era. As a result, this curve also illustrates the $y$-dependence of $\Omega_{\rm tot}$ in this case. By contrast, for all other cases, the total abundance $\Omega_{\rm tot}$ is $y$-independent.
• Figure 5: The tower fraction $\eta$ after all dark-matter modes have "turned on" and entered the present matter-dominated epoch, plotted as a function of $y$ for three different regimes of misalignment production: (a) instantaneous turn-on, in which case $\Omega_\lambda\sim {\tilde{\lambda}}^2 A_\lambda^2$; (b) staggered turn-on during a radiation-dominated era, in which case $\Omega_\lambda\sim {\tilde{\lambda}}^{1/2} A_\lambda^2$; and (c) staggered turn-on during a reheating or matter-dominated era, in which case $\Omega_\lambda\sim A_\lambda^2$. In each case we see that $\eta\to 0$ as $y\to \infty$, while $\eta$ approaches a fixed maximum value $\eta_{\rm max}$ as $y\to 0$.