Higher Order Slow-Roll Predictions for Inflation
  We study the WKB approximation beyond leading order for cosmological perturbations during inflation. To first order in the slow-roll parameters, we show that an improved WKB approximation leads to analytical results agreeing to within 0.1% with the standard slow-roll results. Moreover, the leading WKB approximation to second order in the slow-roll parameters leads to analytical predictions in qualitative agreement with those obtained by the Green's function method. 
R. Casadio, F. Finelli, M. Luzzi, G. Venturi