Constraints on a scale invariant power spectrum from superinflation in loop quantum cosmology

The computation of the spectrum of primordial perturbations, generated by a scalar field during the superinflationary phase of loop quantum cosmology, is revisited. The calculation is performed for two different cases. The first considers the dynamics of a massless field and it is found that scale invariance can only be achieved under a severe fine-tuning. The second assumes that the field evolves with a constant ratio between kinetic and potential energy, i.e. in a scaling solution. In this case, near scale invariance is a generic feature of the theory if the field rolls in a steep self-interaction potential.