Dark matter direct detection with accelerometers

The mass of the dark matter particle is unknown, and may be as low as $\sim 10^{-22}\mathrm{eV}$. The lighter part of this range, below $\sim \mathrm{eV}$, is relatively unexplored both theoretically and experimentally but contains an array of natural dark matter candidates. An example is the relaxion, a light boson predicted by cosmological solutions to the hierarchy problem. One of the few generic signals such light dark matter can produce is a time-oscillating, equivalence-principle-violating force. We propose searches for this using accelerometers, and consider in detail the examples of torsion balances, atom interferometry, and pulsar timing. These approaches have the potential to probe large parts of unexplored parameter space in the next several years. Thus such accelerometers provide radically new avenues for the direct detection of dark matter.

Figure 1

A torsion pendulum for dark matter direct detection (figure adapted from Ref. [81]). The dark matter field directly induces an equivalence-principle-violating acceleration on the test masses, resulting in an oscillating twist in the pendulum. The twist angle is measured by observing the deflection of a laser reflected from the mirror.

Figure 2

Estimated reach of searches for $B-L$-coupled vector DM. Solid blue curves correspond to the torsion pendulum setups discussed in Sec. 5a. Dashed red curves correspond to atom interferometers with acceleration sensitivities of $10^{-13}$, $10^{-15}$, and $10^{-18}\mathrm{g}{\mathrm{Hz}}^{-1/2}$, as discussed in Sec. 5b. Thin green curves correspond to the existing EPTA (upper) and upcoming SKA (lower) pulsar timing arrays, as discussed in Sec. 5d. The orange curve shows our estimate of the reach of Advanced LIGO, as discussed in Sec. 5a4. The shaded region shows bounds from static EP tests using torsion pendulums [63]. For masses below $\sim 10^{-22}\mathrm{eV}$ the field cannot make up all of the dark matter due to its effect on structure formation; this bound may be improved in the future, as discussed in Sec. 5e. Additional bounds from black-hole superradiance may apply if the vector has no self interactions, as discussed in Sec. 5e. We have not shown estimates for the sensitivity of lunar laser ranging to DM, but even existing data is potentially powerful (see Sec. 5c).

Figure 3

Estimated reach of searches for scalar DM coupled through the Higgs portal, $\mathcal{L}\supset b\varphi |H{|}^2$. The blue, red and green curves and the yellow shaded region are as in Fig. 2. The shaded green region is excluded by fifth-force constraints from lunar laser ranging [81, 84], independent of whether the scalar is DM. The shaded purple region was excluded by the search for scalar DM in atomic clock data [64]. The gray line ($m=b$) shows the approximate boundary above which the scalar mass is fine-tuned. As discussed in Sec. 4c, there is an $\mathcal{O}(1)$ theory uncertainty in the degree of EP violation of the coupling to nuclei, which affects both the static EP-test bounds and the projections for atom interferometer and torsion balance tests.

Figure 4

Estimated reach of searches for scalar DM coupled through $\mathcal{L}\supset g_{\varphi ee}\varphi \overline{e}e$. The blue, red and green curves and the yellow shaded region are as in Fig. 2. Above the gray line the scalar mass is fine-tuned if the cutoff $\mathrm{\Lambda }$ is above $\sim \mathrm{TeV}$.