Second-Order Corrections to the Power Spectrum in the Slow-Roll   Expansion with a Time-Dependent Sound Speed
  We extend Green's function method developed by Stewart and Gong to calculate the power spectrum of density perturbation in the case with a time-dependent sound speed, and explicitly give the power spectrum and spectral index up to second-order corrections in the slow-roll expansion. The case of tachyon inflation is included as a special case. 
Hao Wei, Rong-Gen Cai and Anzhong Wang