Superheavy Thermal Dark Matter

We propose a mechanism of elementary thermal dark matter with a mass up to $10^{14}\mathrm{GeV}$, within a standard cosmological history, whose relic abundance is determined solely by its interactions with the standard model, without violating the perturbative unitarity bound. The dark matter consists of many nearly degenerate particles which scatter with the standard model bath in a nearest-neighbor chain, and maintain chemical equilibrium with the standard model bath by in-equilibrium decays and inverse decays. The phenomenology includes super heavy elementary dark matter and heavy relics that decay at various epochs in the cosmological history, with implications for the cosmic microwave background, structure formation, and cosmic ray experiments.

Figure 1

Freeze-out mechanism: the dark matter consists of many nearly degenerate particles which scatter with the standard model bath in a nearest-neighbor chain and maintain chemical equilibrium with the standard model bath by in-equilibrium decays and inverse decays.

Figure 2

Relic abundance of each particle with temperature evolution. Here the masses are assumed to be degenerate, and the decay rate of ${\chi }_N$ is chosen as ${\mathrm{\Gamma }}_N={10}^{2}H(m)$ to ensure that it decays in-equilibrium. The horizontal dashed line is the observed relic abundance of DM, while the solid black curve is the equilibrium abundance. The orange solid line is the abundance for ${\chi }_{10}$, which is the particle at the end of the chain in this example, while the other colored lines give the density for ${\chi }_i$ ($i=1,\dots ,9$). In the inset plot, the red dots show the distribution of relic densities at $x=2\times {10}^4$, normalized with $Y_1$, while the dashed line shows corresponding analytic estimate, Eq. (14).

Figure 3

Number of dark matter particles versus DM mass. The colored solid lines depict the minimal number of particles when ${\chi }_1$ decays through the chain [see Eq. (18)], while the gray solid lines depict the same within an explicit model [see Eq. (25)]. For both, we require that ${\tau }_1>{10}^{27}\sec$. The purple line corresponds to ${\chi }_1$ decay into $2N$ identical SM particles, while the green line corresponds to a pair of $N$ identical SM particles in the final state. The dashed lines are contours of $\alpha$ that reproduce the observed relic abundance, when the cross section of chain reaction is parametrized as $⟨\sigma v⟩={\alpha }^2/m_{\chi }^2$; this contour is model independent.