Quantum effect on luminosity-redshift relation

There are many different proposals for a theory of quantum gravity. Even leaving aside the fundamental difference among theories such as the string theory and the non-perturbative quantum gravity, we are still left with many ambiguities (and/or parameters to be determined) with regard to the choice of variables, the choice of related groups, etc. Loop quantum gravity is also in such a state. It is interesting to search for experimental observables to distinguish these quantum schemes. This paper investigates the loop quantum gravity effect on luminosity-redshift relation. The quantum bounce behavior of loop quantum cosmology is found to result in multivalued correspondence in luminosity-redshift relation. And the detail multivalued behavior can tell the difference of different quantum parameters. The inverse volume quantum correction does not result in bounce behavior in this model, but affects luminosity-redshift relation also significantly.