Pre-inflation models and WMAP data
  The effect of pre-inflation physics on the power spectrum of scalar perturbations is estimated and there is a possibility that the pre-inflation physics explains the Wilkinson Microwave Anisotropy Probe data if the length of inflation is near 60 e-folds. Considering various pre-inflation models with radiation-dominated or matter-dominated periods before inflation, the power spectrum of curvature perturbations for large scales is calculated, and the spectral index and running spectral index are derived. 
Shiro Hirai