First look at continuous spin gravity: Time delay signatures

We consider the possibility that gravity is mediated by "continuous spin" particles, i.e.~ massless particles whose invariant spin scale $\rho_g$ is non-zero. In this case, the primary helicity-2 modes of gravitational radiation on a Minkowski background mix with a tower of integer-helicity partner modes under boosts, with $\rho_g$ controlling the degree of mixing. We develop a formalism for coupling spinless matter to continuous spin gravity at linearized level. Using this formalism, we calculate the time-delay signatures induced by gravitational waves in an idealized laser interferometer detector. The fractional deviation from general relativity predictions is $O(\rho_g/\omega)$ for gravitational wave frequencies $\omega >\rho_g$, and the effects of waves with $\omega \lesssim \rho_g$ are damped. The precision and low frequency ranges of gravitational wave detectors suggest potential sensitivity to spin scales at or below $\sim 10^{-14}$ eV at ground-based laser interferometers and $\sim 10^{-24}$ eV at pulsar timing arrays, motivating further analysis of observable signatures.