A model of polymer gravitational waves: theory and some possible observational consequences

We propose a polymer quantization scheme to derive the effective propagation of gravitational waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. These waves, which may originate from a high energy source, are a consequence of the dynamics of the gravitational field in a linearized low-energy regime. A novel method of deriving the effective Hamiltonian of the system is applied to overcome the challenge of polymer quantizing a time-dependent Hamiltonian. Using such a Hamiltonian, we derive the effective equations of motion and show that (i) the form of the waves is modified, (ii) the speed of the waves depends on their frequencies, and (iii) quantum effects become more apparent as waves traverse longer distances.