The Matter Bounce Scenario in Loop Quantum Cosmology

8 pagesIn the matter bounce scenario, a dust-dominated contracting space-time generates scale-invariant perturbations that, assuming a nonsingular bouncing cosmology, propagate to the expanding branch and set appropriate initial conditions for the radiation-dominated era. Since this scenario depends on the presence of a bounce, it seems appropriate to consider it in the context of loop quantum cosmology where a bouncing universe naturally arises. It turns out that quantum gravity effects play an important role beyond simply providing the bounce. Indeed, quantum gravity corrections to the Mukhanov-Sasaki equations significantly modify some of the results obtained in a purely classical setting: while the predicted spectra of scalar and tensor perturbations are both almost scale-invariant with identical small red tilts in agreement with previous results, the tensor to scalar ratio is now expected to be $10^{-4}$, which is much smaller than the original classical prediction. Finally, for the predicted amplitude of the scalar perturbations to agree with observations, the critical density in loop quantum cosmology must be of the order $10^{-9} \rho_{\rm Pl}$