Loop quantum gravity corrections to gravitational wave dispersion

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.

Figure 1

Dispersion relation for gravitational waves in the presence of inverse volume corrections.

Figure 2

Dispersion relation in the presence of holonomy corrections. The classical dispersion relation is approached as the background energy density decreases.