Searching for spin-2 ULDM with gravitational waves interferometers

The detection of gravitational waves from merging binaries has ushered in the era of gravitational wave interferometer astronomy. Besides these strong, transient, calamitous events, much weaker signals can be detected if the oscillations are nearly monochromatic and "continuous", that is, coherent over a long time. In this work we show that ultra-light dark matter of spin two, owing to its universal coupling $\alpha$ to Standard Model fields, generates a signal that is akin to but distinct from a continuous gravitational wave. We show that this signal could be detected with current and planned gravitational wave interferometers. In the event of a null detection, current facilities could constrain the coupling to be below $\alpha\sim10^{-7}$ for frequencies of tens of Hz, corresponding to dark matter masses around the $10^{-13}$ eV mark. Future facilities could further lower these upper limits and extend them to smaller masses down to $10^{-18}$ eV. These limits would be the most stringent bounds on the spin-2 Yukawa fifth force strength, parametrised by $\alpha$, in the frequency ranges accessible by gravitational wave interferometers. The implementation of this type of searches for gravitational wave interferometers would therefore further our grasp of both dark matter and gravity.