Stewart-Lyth Inverse Problem

Abstract

In this paper the Stewart-Lyth inverse problem is introduced. It consists of solving two non-linear differential equations for the first slow-roll parameter and finding the inflaton potential. The equations are derived from the Stewart--Lyth equations for the scalar and tensorial perturbations produced during the inflationary period. The geometry of the phase planes transverse to the trajectories is analyzed, and conclusions about the possible behaviour for general solutions are drawn.

16 pages, 11 figures, RevTeX; updated to match accepted version

References in corpus (4)

• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• Reconstructing the Inflaton Potential --- an Overview
• Accurate determination of inflationary perturbations
• Reconstructing the inflaton potential for an almost flat COBE spectrum

Cited by in corpus (10)

• WMAPping inflationary physics
• Monte Carlo reconstruction of the inflationary potential
• Inflationary potentials yielding constant scalar perturbation spectral indices
• Inflationary scenarios with scale-invariant spectral tensorial index
• Tensor to scalar ratio of perturbation amplitudes and inflaton dynamics
• Inflation with a constant ratio of scalar and tensor perturbation amplitudes
• Troubles for observing the inflaton potential
• Further evidences for a generic Universe
• An outlier-resistant $\kappa$-generalized approach for robust physical parameter estimation
• Sketching the inflaton potential