Inflationary Dynamics Reconstruction via Inverse-Scattering Theory

TL;DR

This paper introduces a novel inverse-scattering approach using the Gel'fand-Levitan method to reconstruct the inflationary universe's dynamics from primordial power spectra, applicable to slow-roll and non-slow-roll scenarios.

Contribution

It applies inverse-scattering theory to cosmology, enabling reconstruction of inflationary parameters from observational data, a novel approach in the field.

Findings

Successfully reconstructs the inflaton horizon from scalar spectra

Reconstructs Hubble parameter with tensor spectrum data

Demonstrates method for slow-roll and non-slow-roll inflation scenarios

Abstract

The evolution of inflationary fluctuations can be recast as an inverse scattering problem. In this context, we employ the Gel'fand-Levitan method from inverse-scattering theory to reconstruct the evolution of both the inflaton field freeze-out horizon and the Hubble parameter during inflation. We demonstrate this reconstruction procedure numerically for a scenario of slow-roll inflation, as well as for a scenario which temporarily departs from slow-roll. The field freeze-out horizon is reconstructed from the accessible primordial scalar power spectrum alone, while the reconstruction of the Hubble parameter requires additional information from the tensor power spectrum. We briefly discuss the application of this technique to more realistic cases incorporating estimates of the primordial power spectra over limited ranges of scales and with specified uncertainties.