Dark matter with density-dependent interactions

The decay and annihilation cross sections of dark matter particles may depend on the value of a chameleonic scalar field that both evolves cosmologically and takes different values depending on the local matter density. This possibility introduces a separation between the physics relevant for freeze-out and that responsible for dynamics and detection in the late universe. We investigate how such dark sector interactions might be implemented in a particle physics Lagrangian and consider how current and upcoming observations and experiments bound such dark matter candidates. A specific simple model allows for an increase in the annihilation cross section by a factor of ${10}^6$ between freeze-out and today, while more complicated models should also allow for scattering cross sections near the astrophysical bounds.

Figure 1

Tree-level $\psi$ annihilation diagrams. The massive vector boson $A$ is a wavy line, and the scalar $h$ is a dashed line. Annihilations to $A+A$ and $h+h$ via $\eta$ exchange and annihilations to final-state $\eta$ particles are suppressed by large-mass factors.

Figure 2

Ladder diagrams for dark matter annihilation (left) and scattering (right).

Figure 3

Tree-level $h$ decay.

Figure 4

1-loop $A$ decay. Only the first diagram is nonzero.

Figure 5

Scan of parameter space. Blue points indicate sets of parameters that satisfy all constraints, except (for most points) for having a negligible $A$ energy density. Red points do not satisfy the scattering cross section bound $\sigma /{\tilde{m}}_{\psi }<0.1{\mathrm{cm}}^2/\mathrm{g}$. Green points do not satisfy the adiabatic condition in (51) and should be solved with the coupled differential equations.

Figure 6

The number of $A$ decays per particle between freeze-out and BBN. Points above the horizontal line at 1 indicate that all $A$ particles should have decayed and thus do not contribute significantly to the energy budget of the Universe.

Figure 7

The evolution of $\varphi$ (upper left), $Y$ (upper right), ${\tilde{m}}_{\psi }$ (lower left), and $\tilde{f}$ (lower right) as a function of $T$ in GeV for the model with $m_{\psi }=123\mathrm{GeV}$. The red, dotted line indicates the approximate dark matter freeze-out temperature.

Figure 8

The evolution of the annihilation cross section $⟨\sigma v⟩$ (left) and the scattering cross section $\sigma /{\tilde{m}}_{\psi }$ (right) as a function of $T$ in GeV with $m_{\psi }=123\mathrm{GeV}$. The red, dotted line indicates the approximate dark matter freeze-out temperature.

Figure 9

Feynman rules for $h$ (dashed line), $\psi$ (solid line), $A_{\mu }$ (wavy line), and $\eta$ (dotted line). We include the Yukawa interaction with $\psi$ and $\eta$, which is relevant for the 1-loop $A$-decay amplitude in (87), but other $\eta$-interaction vertices are not shown. All parameters labeled by a tilde are evaluated at ${\varphi }_c$.