Constraints on a scale invariant power spectrum from superinflation in   LQC
  The computation of the spectrum of primordial perturbations, generated by a scalar field during the super-inflationary 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. 
D. J. Mulryne and N. J. Nunes