Anomaly-free scalar perturbations with holonomy corrections in loop
  quantum cosmology
  Holonomy corrections to scalar perturbations are investigated in the loop
quantum cosmology framework. Due to the effective approach, modifications of
the algebra of constraints generically lead to anomalies. In order to remove
those anomalies, counter-terms are introduced. We find a way to explicitly
fulfill the conditions for anomaly freedom and we give explicit expressions for
the counter-terms. Surprisingly, the "new quantization scheme" naturally arises
in this procedure. The gauge invariant variables are found and equations of
motion for the anomaly-free scalar perturbations are derived. Finally, some
cosmological consequences are discussed qualitatively.
