  Cosmological tensor perturbations equations are derived for Hamiltonian
cosmology based on Ashtekar's formulation of general relativity, including
typical quantum gravity effects in the Hamiltonian constraint as they are
expected from loop quantum gravity. This translates to corrections of the
dispersion relation for gravitational waves. The main application here is the
preservation of causality which is shown to be realized due to the absence of
anomalies in the effective constraint algebra used.
