From Non-trivial Geometries to Power Spectra and Vice Versa

TL;DR

This paper reviews a formalism that derives the primordial power spectra for inflationary models with complex geometries, providing explicit formulas and an algorithm to reconstruct models from observed spectra, especially for models with potential features.

Contribution

It introduces a new formalism that accounts for non-constant slow-roll parameters and offers a reconstruction algorithm from observed power spectra.

Findings

Analytic expressions for power spectra with geometric dependence.

Successful application to models with potential features.

Excellent agreement with observed spectra.

Abstract

We review a recent formalism which derives the functional forms of the primordial -- tensor and scalar -- power spectra of scalar potential inflationary models. The formalism incorporates the case of geometries with non-constant first slow-roll parameter. Analytic expressions for the power spectra are given that explicitly display the dependence on the geometric properties of the background. Moreover, we present the full algorithm for using our formalism, to reconstruct the model from the observed power spectra. Our techniques are applied to models possessing "features" in their potential with excellent agreement.