Gravitational waves with generalized holonomy corrections

The cosmological tensor perturbation equation with generalized holonomy corrections is derived in the framework of effective loop quantum gravity. This results in a generalized dispersion relation for gravitational waves, encompassing holonomy corrections. Furthermore, we conduct an examination of the constraint algebra concerning vector modes with generalized holonomy corrections. The requirement of anomaly cancellation for vector modes imposes constraints on the possible functional forms of the generalized holonomy corrections. What's more, we estimate the theoretical value of the effective graviton mass and discuss the potential detectability of this effective mass in future observations.