“School of Astronomy”
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Paper IPM / Astronomy / 16660  


Abstract:  
The linearized Einstein field equations provide a lowenergy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization scheme to derive the effective propagation of such waves on a classical FriedmannLemaitreRobertsonWalker (FLRW) spacetime. To overcome the challenge of polymer quantizing a timedependent Hamiltonian, we rewrite such a Hamiltonian in a timeindependent manner in the extended phase space, polymerize it, and then transform it back to the usual phase space. In this way we obtain a timedependent polymer Hamiltonian for the gravitational waves. We then 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
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