Sound of Dark Matter: Searching for Light Scalars with Resonant-Mass Detectors

The fine-structure constant and the electron mass in string theory are determined by the values of scalar fields called moduli. If the dark matter takes on the form of such a light modulus, it oscillates with a frequency equal to its mass and an amplitude determined by the local dark-matter density. This translates into an oscillation of the size of a solid that can be observed by resonant-mass antennas. Existing and planned experiments, combined with a dedicated resonant-mass detector proposed in this Letter, can probe dark-matter moduli with frequencies between 1 kHz and 1 GHz, with much better sensitivity than searches for fifth forces.

Figure 1

Scalar field parameter space, with mass $m_{\varphi }$ and corresponding DM oscillation frequency $f_{\varphi }=m_{\varphi }/2\pi$ on the bottom and top horizontal axes, and couplings of both an electron mass modulus ($d_i=d_{m_e}$) and electromagnetic gauge modulus ($d_i=d_e$) on the vertical axis. Natural parameter space for a 10-TeV cutoff is depicted in green, while the other regions and dashed curves represent 95% C.L. limits from fifth-force tests (“5F,” gray), equivalence-principle tests (“EP,” orange), atomic spectroscopy in dysprosium (“Dy,” purple), and low-frequency terrestrial seismology (“Earth,” black). The blue curve shows the projected $\mathrm{SNR}=1$ reach of a proposed resonant-mass detector—a copper-silicon (Cu-Si) sphere 30 cm in radius—after 1.6 y of integration time, while the red curve shows the reach for the current AURIGA detector with 8 y of recasted data. Rough estimates of the 1-y reach of a proposed DUAL detector (pink) and several harmonics of two piezoelectric quartz resonators (gold points) are also shown.

Figure 2

Schematic of the proposed setup: a Cu-Si sphere whose surface displacement is monitored by a Fabry-Pérot (FP) interferometer. Elements encircled by the dotted lines are independently suspended and isolated from vibrations.

Figure 3

Strain reach $|h|$ at $\mathrm{SNR}=1$ as a function of frequency $f$ after an integration time $t_{\mathrm{int}}=5\times 10^7\mathrm{s}$ (thick blue curve), consisting of a 5% fractional frequency scan by varying the temperature between 4 and 100 K in increments, each $t_{\text{shot}}=10^3\mathrm{s}$ long. Reach for one “shot” at 4 K is shown by the thin blue curve (up to the third harmonic, for clarity). Equivalence-principle and fifth-force exclusions are shown in orange and gray, while strains below the green line are natural for an electron Yukawa modulus with a 10-TeV cutoff.