Reconstructing the Inflaton Potential

A review is presented of recent work by the authors concerning the use of large scale structure and microwave background anisotropy data to determine the potential of the inflaton field. The importance of a detection of the stochastic gravitational wave background is emphasised, and some preliminary new results of tests of the method on simulated data sets with uncertainties are described. (Proceedings of ``Unified Symmetry in the Small and in the Large'', Coral Gables, 1994)Comment: 13 pages, uuencoded postscript file with figures included (LaTeX file available from ARL), FERMILAB-Conf 94/189

Reconstructing Single Field Inflationary Actions From CMBR Data

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.Comment: 33 pages, 3 figures: v3 - References adde

Reconstructing the Inflaton Potential --- an Overview

We review the relation between the inflationary potential and the spectra of density (scalar) perturbations and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton potential from observations. The spectra provide a potentially powerful test of the inflationary hypothesis; they are not independent but instead are linked by consistency relations reflecting their origin from a single inflationary potential. To lowest-order in a perturbation expansion there is a single, now familiar, relation between the tensor spectral index and the relative amplitude of the spectra. We demonstrate that there is an infinite hierarchy of such consistency equations, though observational difficulties suggest only the first is ever likely to be useful. We also note that since observations are expected to yield much better information on the scalars than on the tensors, it is likely to be the next-order version of this consistency equation which will be appropriate, not the lowest-order one. If inflation passes the consistency test, one can then confidently use the remaining observational information to constrain the inflationary potential, and we survey the general perturbative scheme for carrying out this procedure. Explicit expressions valid to next-lowest order in the expansion are presented. We then briefly assess the prospects for future observations reaching the quality required, and consider a simulated data set that is motivated by this outlook.Comment: 69 pages standard LaTeX plus 4 postscript figures. Postscript version of text in landscape format (35 pages) available at http://star-www.maps.susx.ac.uk/papers/infcos_papers.html Modifications are a variety of updates to discussion and reference