Reconstructing single-field inflationary actions from cosmic microwave backgroundradiation data**This work was supported by the US Department of Energy.

Abstract

This paper describes a general program for deriving the action of single-field inflationmodels with non-standard kinetic energy terms using cosmic microwave backgroundradiation power spectrum data. This method assumes that an action depends on aset of undetermined functions, each of which is a function of either the inflatonwavefunction or its time derivative. The scalar, tensor and non-Gaussianity of thecurvature perturbation spectrum are used to derive a set of reconstruction equationswhose solution set can specify up to three of the undetermined functions. Themethod is then used to find the undetermined functions in various types of actionassuming power law type scalar and tensor spectra. In actions that contain onlytwo unknown functions, the third reconstruction equation implies a consistencyrelation between the non-Gaussianity, sound speed and slow roll parameters. Inparticular we focus on reconstructing a generalized Dirac–Born–Infeld actionwith an unknown potential and warp factor. We find that for realistic scalar andtensor spectra, the reconstructed warp factor and potential are very similar to thetheoretically derived result. Furthermore, physical consistency of the reconstructed warpfactor and potential imposes strict constraints on the scalar and tensor spectralindices.