Reconstructing single-field inflationary actions from cosmic microwave background radiation data

This paper describes a general program for deriving the action of single-field inflation models with non-standard kinetic energy terms using cosmic microwave background radiation power spectrum data. This method assumes that an action depends on a set of undetermined functions, each of which is a function of either the inflaton wavefunction or its time derivative. The scalar, tensor and non-Gaussianity of the curvature perturbation spectrum are used to derive a set of reconstruction equations whose solution set can specify up to three of the undetermined functions. The method is then used to find the undetermined functions in various types of action assuming power law type scalar and tensor spectra. In actions that contain only two unknown functions, the third reconstruction equation implies a consistency relation between the non-Gaussianity, sound speed and slow roll parameters. In particular we focus on reconstructing a generalized Dirac-Born-Infeld action with an unknown potential and warp factor. We find that for realistic scalar and tensor spectra, the reconstructed warp factor and potential are very similar to the theoretically derived result. Furthermore, physical consistency of the reconstructed warp factor and potential imposes strict constraints on the scalar and tensor spectral indices.