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 $O({\rho }_g\mathrm{/}\omega )$ 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.