  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.
