Oscillations and parity violation in gravitational wave background from extra tensor modes

Abstract Spectator fields which provide additional tensor degrees of freedom, on top of the standard metric tensor perturbations, can produce significant amounts of gravitational waves (GWs). Employing the effective field theory approach for spin-2 fields, we identify a characteristic prediction of this class of scenarios: whenever the spin-2 sector undergoes a localized non-adiabatic evolution during inflation, the linear mixing between the metric and extra tensor modes transmits this feature to the GW spectrum as oscillations in scale. The leading oscillation period is determined analytically by the time at which the localized feature occurs and by the propagation speed of the extra tensor mode outside the feature. The same coupling, when sufficiently strong, also drives an in-time oscillation of the superhorizon modes that is reminiscent of neutrino flavor oscillations. Moreover, parity-violating operators in the spin-2 EFT can imprint chiral signatures on the resulting GW background. Such chirality is an important possible signature for features in the non-minimal kinetic coupling, and becomes closely tied to large observable enhancement for features in the sound speed of the extra tensor mode. We consider a concrete scenario in which the spin-2 field generates observable chiral GWs with characteristic oscillatory patterns. These results identify robust signatures that can be probed with future GW detectors, while the exact amplitude, peak position, and parameter values remain model dependent.