Reconstructing Single Field Inflationary Actions From CMBR Data

TL;DR

This paper presents a method to reconstruct single field inflationary actions with nonstandard kinetic terms from CMBR data, enabling detailed insights into inflation models and their parameters.

Contribution

It introduces a general reconstruction framework for inflation actions using CMBR spectra, including a specific application to generalized DBI models with potential and warp factor.

Findings

Reconstructed warp factor and potential closely match theoretical predictions.

Derived a consistency relation linking non-gaussianity, sound speed, and slow roll parameters.

Imposed constraints on spectral indices based on reconstructed functions.

Abstract

This paper describes a general program for deriving the action of single field inflation models with nonstandard kinetic energy terms using CMBR 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 wave function 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 actions 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-gaussianty, sound speed and slow roll parameters. In particular we focus on reconstructing a generalized DBI 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.